I’m not convinced that this is the case. While there’s no predisposition to hate gays in particular, the prevalence of tribal warfare in human history suggests that we do have some default predisposition to hate otherness, which includes homosexuality. In civilized society, such behavior is repressed (and ideally stamped out) by education and exposure. Even secularism, which has been suggested earlier in the thread to be the best correlate for LGBTQ acceptance, is a proxy (or perhaps a consequence of) higher rates of education and cultural exposure. This explains the demographics that were mentioned earlier in the thread regarding the prevalent opposition to gay rights among religiously disparate groups (Evangelical Christians, Muslims, and [religiously unspecified but probably Orthodox] Russians). All of these groups are either under-educated compared to the Western norm, underexposed to LGBT people (see here for statistics on Russia; for those who can’t read it, 80% of respondents believe they have never met a homosexual person), or both. This, combined with the previously cited preponderance of Jews, Buddhists, and Hindus who support equal rights for sexual minorities, suggests that a combination of social exposure and education drive tolerance for “other” viewpoints, rather than the absence of religion or some other social vector.
I don’t think it’s fair to compare the views of Muslim immigrants to America with those of Muslims in Bangladesh (I’m singling out this comment for reply, but throughout the thread I’ve seen references to American Muslims that appeared to generalize opinions to the rest of the world). As you mentioned yourself, US Muslims are distinct in being able to immigrate, which is likely due to having a higher level of education. This satisfies one of the criteria which I mentioned above, which significantly cuts down on the percentage of adherents who fail both requirements (education and exposure). Beyond this I don’t have any statistics, but I would assume that exposure to minority cultures upon arrival significantly moderates the immigrants’ outlook, thereby satisfying the second criterion. Anecdotally, I have seen this with a friend of mine whose views on violent Palestinan resistance became much more pacifist upon getting to know myself and several other Jews.
Regarding what to do to assuage Valteron and panache45’s concerns: I’m curious as to what would be constitutional regarding profiling in the immigration process (for both Canada and the US). If the task of immigration is solely to minimize the number of people entering the country who harbor bigoted views, then it seems that the most efficient filter (barring sealed borders) would be one that tar gets certain demographics for intense personal scrutiny during interviews on this topic. These demographics would include educated people coming from generally intolerant societies, and poor people coming from more tolerant societies. While this policy would theoretically treat Russians Atheists, Ugandan Christians, and Saudi Muslims the same, I’m curious if it could be legally applied. Denying entry to those who are opposed to equal rights for ethnic and sexual minorities but have never advocated physical violence would infringe upon freedom of expression (do potential immigrants have any semblance of this right?) Of course, if there are enough resources to extensively interview all immigrants to elucidate their views on minority cultures, this would be the more optimal solution.
The question of what to do with domestic radicals is more difficult. Other than intensively monitoring public communications (e.g. message boards dedicated to white supremacy, Islamism, etc), I have no short term ideas. In the long term, increased funding of K-12 education combined with a mandatory and early diversity-oriented curriculum would produce more educated and empathetic immigrants who would be less prone to violence, but the lag time between implementation and results would be measured in decades.