That's another interesting issue. I also studied about Burakumin in uni, and when I finally moved to Japan, I found out that nobody will talk about Burakumin. It's not like I was going around interviewing people and asking their opinions, but every time the topic would come up one way or another, the Japanese person would always shut down or change the topic. Even people I considered to be good friends.
I've said this on GAF before, but I had a buddy that was teaching a cultural studies class at a local university here in Hiroshima, and the Burakumin issue was on the curriculum. One of the students complained to their parents and the university forced my friend to remove that lesson from the syllabus.
And finally, my Japanese mother-in-law had absolutely no problems with her daughter marrying me, a white American, but when my wife's older sister got engaged last year, mom-in-law did one of those illegal background checks mentioned in the OP to make sure that her husband wasn't of Burakumin ilk. Really, really messed up. She's a real piece of work, though. When my wife and I told her of the Korean ferry disaster last month, the first thing she said was, "Were there any Japanese on board?" Unfortunately, this kind of response is fairly typical.