Supernatural beings or whatever, the denial of a personal, creator god is FUNDAMENTAL to being truly a Buddhist. Supernatural beings in Buddhism, are nothing but other forms of reincarnation, and have no magical influence over the physical world. In the end, becoming a buddha is becoming the ultimate state of being. If you know your history, you will find that the main struggle between Buddhism and Hinduism in terms of philosophy when Buddhism came into the being was the radical concept of denying the existence of personal gods, creator gods, and gods that can magically influence the world. And based off of that is a very important concept of natural cause and effect, aka kharma, which explains why things happen to you the way they do, and why you're born the way you are. Kharma in Buddhism is much different from the Vedic Hindu belief in that it is thought as well as action, althought thought is more important, that is the root of all kharma, as opposed to action alone.
And finally, getting to reason why Buddhism exists as a religion in the first place ? It is so that people can learn a pathway that individual themselves can mold themselves and practice to reduce suffering at its roots, ie eliminating causes of suffering, broadly categorized as hate, anger, attachments and ignorance of the way the universe works. Therefore, I would argue that in denying a creator and a personal god, is quite important to being a Buddhist. To acheive that enlightenment, you can't be relying on a personal god who intervenes to be the one who decided where you were born, why you are the way you are, and determine where you will go after death. Its quite important to deny a creator god in Buddhism, because its the foundation of everything else in the religion for crying out loud, from the philosophy all the way up to why you go shave your head, retreat into the mountains and meditate all day.
If you want to be a so called Christian Buddhist, you have to first of all believe in God, and Jesus Christ and the resurrection and that in believing in him, you will be saved and go to heaven. Then on the otherside, I'm not quite sure how that can fit with there is no creator god, and that your own actions are the only thing that determine what will happen to you. Again, I can't come to see how the 2 religions have any kind of reconcillation unless you decide to misconstrue it like some hippie era dude to your own liking. Then it really becomes some alternative religion that is neither Christianity nor Buddhism - it may have resemblance, but it really isn't either. But you might be interested to know that Hindus simply absorb Christianity into themselves since they can just make Jesus another avatar of their gods.
Abrahamic Mosaic religions all believe in the same god, however, they all believe in different profits, messiahs, and such. The thing is that they can't decide on which one of them is the true one, and what is the correct way to worship God. Many of the fundamentals between them are shared in the Old Testament. The main problem is the texts that come afterwards. And for them, the way each religion's texts are written, they set themselves up to deny and condemn any other way of worshipping God. The oppression of various sects of protestantism and Catholism was considered by the intellects of the time, and the rulers to be of a similar idea, that it wrong to worship God any other way than the way that they believe. My personal bias is that all of this stuff is totally irrational to start with, but to those irrational individuals its reason enough. Again, the bottom line is that their fundamental difference is that it is evil to worship God any other way than their own way.
On the issue of Buddhist oppression in China during various parts of Chinese history, such is true, but it isn't nearly as dramatic and outrightly violent as culling hundreds of thousands of Christians at once and chopping off all their heads. Much of the oppression of Buddhism in China was pretty short lived, and occured when the court becomes overly influenced by power seeking Daoists, or Confucians who are skeptical of Buddhism because it comes from abroad. If you read the primary sources, many of the Confucian intellects who advocated shutting Buddhism down were really ignorant of the religion as a whole, often making incorrect statements about the teachings, or speculating unreasonable doom and gloom in the case that everyone shaves their heads and retreat into the mountains. Much of the oppression itself was a matter of closing temples, and forcing monks and nuns to return to lay life. In the long run, Buddhism has still caught on in Chinese Middle ages, and is very comparable to the stregnth of Christianity in European middle ages.
And the main reason why Buddhism and Confucianism work together is in the details. To say that Christianity is a cosmos related religion that does not deal with state, and hence it doesn't disturb Confucianism's turf, and therefore it should not contradict is naive. The details is that Buddhism and Confucianism appeal to a SIMILAR CONCEPT of "natural law" off of which ALL OTHER parts of their respective philosophies are derived. Therefore, much of Confucianism and Buddhism come to the same conclusions and reasoning for morality of the mundane world. Buddhism, does not go on to apply this to the state. Confucianism does go on to apply this to the state. Confucianism does not go on to apply this to the afterlife, while Buddhism goes on to explain the afterlife, the cosmos, etc. Therefore, the reason why you can be a Buddhist and a Confucian at the same time, is that in being both, you've covered all your bases. The layman's lifestyle does not change, if not, the humaneness and other virtues are reinforced because now you have 2 philosophies telling you to do the same thing. In terms of government, the Emperor's role is to promote morals, virtues, learning, and forge harmony in his country. Many of China's emperors became Buddhists, because not only does it imply that he should be humane and continue doing the good things he is supposed to be doing (not always performed by every emperor in history, but then thats why they get overthrown), but they too, like other people in China, now have something rational, that fills the void of the cosmos for them, and appeals to the similar fundamental concept of "natural law" with which to do that. Therefore, in a nutshell, Buddhism became quickly adopted in East Asia. In fact, many scholars will argue that it is because of Confucianism, that Buddhism has any place in the world today. If China rejected Buddhism, its migration would have died, and with Theravada Buddhism pretty much dying out in India, and being resticted to mostly Southeast Asia, that would have been that. Its kind of off topic, but Daoism also has many similarities to Buddhism. Although so called religious Daoism has a colorful history of its own conflicts with both Confucianism and Buddhism, but on the otherhand, philosophical Daoism, mostly based off the Dao De Jing, played much of a role in helping Buddhism catch hold. The Dao De Jing kind of talks about natural phenomenon in such a way as to give some wisdom into life, but I can't quite find a word to categorize it, but it has a sense of cosmology to it that isn't quite complete, but has been argued by some scholars to be a factor in helping Buddhism also catch on.
True, Buddhism is meant to be maleable in its appearance, in which it molds into the culture of where it goes. But what this means is that when Buddhism goes to China, the Buddha's statue is sculpted to look like a Chinese man, and he wears Chinese clothes, and the monks wear a variation of Chinese clothing, and the temples are built with Chinese architecture. Likewise, if Buddhism were to enter the west, this means that the Buddha will probaly look more Caucasian, the monks can wear a austere form of western clothing, and the temples will look like churches instead. It does not mean that you compromise teachings to enter a different culture.
So why is it that Christianity, while not overlapping Confucian turf is a problem ? Well, first of all, Christianity, as well as other theistic religions, appeal to the fact that there is a creator god who sets the rules in this universe and he interferes and determines who goes where, and what happens. There is a devine intervention, and one of your primary goals in life is to worship God, and follow his teachings. Implied in that is that kings and emperors need to spend time glorify God and spread his teachings, and that is because God made you emperor, and so you have that obligation. Also, it is implied that you follow God's rules because thats what he wants you to do, and you are not to reason why. If he tells you to kill your son and sacrifice him, that is what you do. Therefore, your faith in God is of utmost importance. So thats just the premise.
As many scholars comment, Confucianism is a highly rational philosophy that uses reasoning to come to the conclusions as to why everything on earth works the way it does and what those implications are for governmental application. First of all, Christianity does not appeal to "natural law." It appeals to divinity, and everything in it is based off of an omnipotent God. Theres nothing natural about it. Second, Christianity, requires an element of faith. Faith is outside the realm of rationality. Confucianism uses only rationality for come to conclusions. Yet another contradiction. Next, while Christianity doesnt directly dictate the state, its reasoning alone threatens how a Confucian society works. The harmony of a nation is acheived when the emperor and his grand secretariat of officials are the most exemplary moral figures in the nation, and that everyone follows their example. The emperor rises or stays in his position because his morality has naturally granted him the heaven's mandate, because the people love him like they love their parents because he is humane and treats them well. Emperors and grand officials like other people are not born perfect, they have to cultivate themselves to be the way the are. When you throw in a God, all of this goes haywire. An interventional God, chooses who goes where. It implies that Emperors were selected by God, as opposed to him naturally becoming or maintaining his position because he is well cultivated. It also implies that people are made the way they are, and self cultivation is an afterthought of your own inborn capacity given by God. It also means that God being the creator of moral rules, must be the most moral example there is, but when Confucians look at the Bible and the Old Testament and see things where God nuking cities out of spite, testing people by telling them to kill their son, among other examples in which Confucians do not look for in a moral character, then question marks start to appear in their minds - or when the hypothetical question of virtuous people like kings of antiquity, King Wen, King Wu, and the Duke of Zhou, or even Confucius himself who did not believe in a God all went to hell along with everyone's parents prior to this. Ancestor veneration doesn't mean much anymore because they're all in hell for being evil heathens. By this time, Confucian scholars are ready to go to war to enact what what Confucianism calls "justified punative wars" to root out a religion that is steeped in what they would consider irrationality, superstition, and falsehood. And if you read the primary sources, it did indeed happen exactly the way I told you, and all the officials in the court pushed for it with the exact same reasoning.
This is just in a nutshell why Confucianism isn't on the same frequency as Christianity. I can probably go on for days, but I think this is pretty darn good. The bottom line I think is still the reasoning. Its simply natural law vs. divinity from which all conflicts stem from. Its good that you're skeptical about it simply being history being a poor explanation, and so I felt it deserved one, but indeed, there is a deeper philsophical reason than it just being history.