The little I know and golfer:
You are probably far more knowledgeable in this area than any other posters here, and your age, experience, and wisdom render your comments noteworthy.
However, In my limited experience with my own family and assisting friends with placing their children in appropriate schools (in Brooklyn), I have not encountered this bigotry that you mention, even in the most yeshivish yeshivos.
Most people want to fit in with the crowd at their children’s schools, so a man who wears a blue shirt would usually not apply to a school where everyone wears white ones.
If he does apply and is rejected, it is most likely not because of an elitist attitude; rather, his wife may not have the requisite level of tznius for that school, or they may have unfiltered internet, and that is against school policy.
I have seen people who are not of the “nouveau yeshivish” class (working or from different backgrounds) be accepted into those schools because they conform to the standards of the yeshivish decision-makers in matters of kedusha, not the color of their shirts.