I am not quite sure of the logic behind openly dismissing the reasons being offered to replace them with your own outsider perspective. It makes it seem like you're uncomfortable with race being important and thus denying its place in any discussion.
Because the reasons offered don't really make a lot of sense. This doesn't mean we must deny race "its place in any discussion." What I object to is this automatic, "It's because they're brown people," point of view, which is simplistic and illogical. There are a number of examples of people in western countries discriminating against immigrants with the same skin color. Also I'm not suggesting that you were the one posting this, it was in response to other posts.
I would say that race is involved in that it groups everyone from a particular background as, when we're talking about Muslim immigrants, radical Muslims. Quite a few people from a Muslim background are secular. Most of the Iraqis I socialize with - not necessarily representative of the average Iraqi - never pray, many drink alcohol and several are secular to the point of being anti-Islam.
Most of these people do not speak English and have not traveled outside of the Middle East much if at all so this isn't just a case of assimilated immigrants. If they went to Europe, because they're from the Middle East and may have a name like Muhammed or Ali, people who are anti-immigrant will likely assume they are radical Muslims but that's far from the case.
With hundreds of thousands of migrants coming into Europe over the last 2 years or so, a number of high-profile terror attacks connected to radical Islam (though for the most part not perpetrated by recent immigrants/migrants) and the global conflict involving radical Islam I find it hard to believe the opposition to Muslim immigration in Europe comes from the fact that they are "brown people," which is also a rather inaccurate way to categorize people from the Middle East who will have a pretty broad range of skin tones but that's become popularized to the point it's hard to get rid of.
I don't know if I would put radical Islam as necessarily the #1 cause of anti-immigration as much as it may be the large numbers of people over the last few years and the cultural differences. It's also useful to distinguish between radical Islam and highly conservative Islam. Just because someone wears a burqa doesn't mean she or the men in her family support violence.
When it does play a part, I think skin color does make people more easily identifiable as part of a separate group. I wouldn't look to it for the primary reason people are opposed to immigrants. As if people would be totally fine with large-scale Muslim immigration if the people were all Chechens or Bosnians.
Tell the difference is an interesting phrase. Sure, I someone with a straight of the spy plane Russian accent pops up next to someone from Chicago tomorrow at Denny's the waitress is going to be able to "tell the difference." But without an immediate comparison source and as long as the just got here yesterday edges have been knocked off that same waitress will just say "had an accent" and if pressed for what kind will likely have to be prompted with samples.
On the other hand, if the person is brown the waitress will lead with that immediately in giving a description and is likely to be unable to provide a second line.
Chicago is an odd example. I don't think people in a huge city who likely see a lot of people of different backgrounds and races every day are likely to jump to assumptions like that.