If someone accepts new ideas as the absolute truth without proof, then that person is not agnostic, seems to me that if the majority were intrinsically agnostic at the dawn of religions then religions would never have become a big thing historically.
That would be an active agnosticism. Some people believe in Christianity but don't press others to. Thus some are actively Christian and would argue for it, while others are passively Christian and generally just accept it as a truth for themselves. Just as some people don't know what to believe
(the definition of agnostic) and would urge others to adopt that view because they find it's the only rational outlook, whereas others would just maintain that view for themselves.
What I said there has nothing to do with imposing beliefs on others, rather the opposite. An agnostic would not find it natural to urge anyone else to adopt their way of thought as there is no way an agnostic can provide sufficient rational grounds to argue that human reason is incapable of deriving truths without rational ground. An agnostic doesn't actively oppose that which cannot be proven, because then (s)he would not be truly agnostic. I don't think what you describe as an active agnostic can exist, it would be a paradox. There's a difference between actively opposing the seemingly un-provable, and to never personally accepting something equally un-provable as the absolute truth.
If we have a situation where every person MUST declare a religious status, whether they even have thought about religion or not, then clearly, passive agnosticism would be the default.
It's a good argument within your definition of agnosticism, but an ism is an ideology, ideologies are not arrived at without relevant deliberate though preceding it. Your example is that someone for the first time in his/her life is forced to choose between multiple complex stories about the world which (s)he has never heard the likes of before that day, and declare one of those stories as part of his/her identity. Without time to decide anything, most persons would declare a random religion, very few would be convinced about the correctness of any of them or even have an opinion regarding whether they are rational or irrational, so most would be undecided about what to actually choose until perhaps years after the initial choice was made.
That person may never take a stance on whether knowledge has to be based on rationality or if feelings can be enough reasoning for knowledge to be valid. If that person in the end decides that feelings are not enough to base knowledge off on, then that person has become agnostic and will most likely stop deliberating seriously on any of the religions (s)he has up to that point identified as based on feelings rather than rationality. Becoming agnostic changes the deliberation from being lost in an impossible choice between equally confounding choices that seems very important to get right, into a realization that the choice no longer seems as pressing or important as one accepts that there are certain questions in life that one can never actually answer, like which one of these are correct for me to choose. So the agnostic would then pretty much stop doubting the initial choice and if allowed to might even stop declaring it as part of their identity. Sure there are those who has practiced a religion for so long when they become agnostic that it would be uncomfortable to live life without the rituals/traditions that was part of practicing that religion, but it would be more of an lifestyle habit than a true conviction.
I don't think anyone is born agnostic, I think most are born as undecided individuals in every and all ways. Becoming an agnostic is to have made a general realization that there are a certain set of factors that qualifies something as undecidable.
Defining agnosticism as simple as (passive agnostic = undecided, active agnostic = "decided when to be undecided") seems crude to me.
Present a religious zealot from the year 649 AD with the question: "decide now if the world is flat or round", a question that zealot never have contemplated before, then clearly, passive agnosticism would be the default.
It just doesn't seem right to water down the meaning of agnosticism like that, you know. Agnosticism is a mindset that zealots just don't have, and if they got it then they would stop being zealots, no.
In that case you shouldn't adopt pretty much any elaborate theory outside of - perhaps - the natural sciences. Not to mention that your own mind could never be considered infallible either. Or even mathematics (just ask Goedel).
Was kinda the extreme case I described, but sure, as long as you have no reason to doubt your own ability to determine if something you see or hear is based on rational thoughts or not, you don't necessarily have to know exactly how it is proven to consider it true, especially if it can be empirically observed day to day, or if you simply know that proper scientific methods is behind that knowledge and consider scientific methods to be based on rationality.
An agnostic could hear a rumour about someone from a trusted source and believe it, perhaps more take into account than believing. People with principles usually break them once in a while without noticing, doesn't mean they don't have those principles in general, just means they are people.