I think it's a stupid stigma, too. Hating something just because it's Japanese sounds pretty racist to me.
I've never really understood that stigma. I haven't had too much contact with it, though. Some of the more popular kids when I was in school had at least some interest in Japanese stuff--Pokemon, some of the other popular anime of the time, etc. I have seen a person or two derisively claiming that they didn't get anime and wouldn't get into it, though.
Part of it, I think, might be how different it is--the language (If it's not dubbed. I feel like dubbed would be much easier to accept, since I think some people would object to having to read while watching TV.), the anime art style and how different it can be from a more Western one. To a certain extent, maybe differing cultural aspects, too? Japan can do lots of little things that Westerners find hard to understand (like the sorts of things you see on the more colorful Japanese game shows, etc.).
Really, I feel like a lot of it probably has to do with how into it the people in question are, though. Or that could be at least as important. I feel like if a person gets into
anything hard and heavy enough, eventually people around them will find it grating and decide to try to deflate them a little. In fairness, to a certain extent that does fall into the realm of manners--it's probably not the best manners to overly push your interests on everyone around you. But I think there might also be a certain...selfish?...inclination to silence people who loudly profess stuff that's completely foreign to you. Maybe it's just a desire to avoid the cognitive "noise" of stuff you don't care about, never will care about.... Or maybe it's kind of a deep social thing, where you don't want to somehow become an "outsider," so you want to squash the appearance of this new thing you know nothing about in order to keep it from spreading?
I could imagine kids maybe picking on people from a foreign country just because they were different, and I'm sure racism can manifest in children if they pick it up from other people. But I don't know if I'd call any of the stuff from earlier "racist," exactly, because I'm not sure that the people who do these things necessarily have anything against the Japanese people themselves. I'm not saying it couldn't/doesn't happen, because I'm sure it does for other races/in other situations, maybe even for the Japanese. But for this discussion, I'm mostly imagining the kinds of school-age stuff I can remember regarding the acceptance of anime/etc.