Though, I don't agree with tarring everyone with the same brush or making generalizations against a group of people because of the actions of one or two or a few, I think people have a right to decide who they want to let into their lives if it makes them feel better (and I hope people who do so understand this when it's done to them too).
I think this is still discrimination based on race though on a personal level and as a reaction to negative experience. Same thing with your cousin's experience. Many people hold such biased views though will not say it out loud.
It's the sort of thing I personally wouldn't be bothered about compared to discrimination in the workplace and other public sectors or if they start inciting hatred, hostility or violence against the group or individual members of the group, for example.
People shouldn't be forced to be friends with anybody and I wouldn't want to be friends with anyone who doesn't want me either.