Specifically about that type of person you mentioned that is against something vehemently until they are personally related to the side of the issue they opposed, I can't help myself but feel more disdain for these individuals than if they had continued holding their prejudiced/bigoted views because their transformation seems incredibly intellectually dishonest. I liken it to the type of person that apologizes profusely after they have been caught red-handed with some wrongdoing, but they never once apologized or confessed during the time they were doing it. In other words, they aren't sorry they did it, they're sorry they got caught doing it.
Maybe my views on the issue are too harsh, but those are my own prejudices. I do think that people can have genuine transformations of views, but it doesn't sit well with me when it only came about because they were cornered into it.
[1] like those republican politicians who are suddenly OK with homosexuality because they find out that one of their kids is homosexual, or many friends who are suddenly the biggest feminists on the Internet because they have daughters. I don't mind, but I do wish they had not been such dicks before having their epiphany.