The only thing I heard was that foreigners were usually turned away from hostess bars if they are not accompanied by a Japanese.
Having walked through Kabuki-cho with just one white buddy (me being of Asian descent, but definitely American), we were openly "recruited" to go into a variety of hostess bars, both in Japanese and English. I've only been to one, it being a mainly gaijin establishment, with women of European, southeast Asian, and even South American descent. Good times.
We also ventured into a couple of places on our own, just to see how people would react, and I'd say it was 50/50.

A group of us would get turned away at nomihodai (all-you-can-drink) sometimes, but that's understandable since we'd drink ourselves stupid and make a scene.
I can't imagine how much worse the scene would have been if our groups had ever been turned away. We never once got turned away from a nomihoudai, even with a heavy majority of foreigners, and I'm sorry to hear that you did. And if drinking yourself stupid and making a scene were any cause for concern, Japanese people wouldn't be allowed in those places either.

Are these only limited to caucasians? Would Asians be in general less "discriminated" in Japan because they are not "white?"
No, they do it to every other race too. A half white, half black friend of mine had a guy come up to her and say repeatedly "brajiru? brajiru?" I mean, I know there's a fair amount of Japanese in Brazil, but is that really the default? I definitely felt like I blended in with everybody else, but that may be due to the fact that I spoke mainly Japanese and spent a lot of time with my host family. Having a Japanese surname doesn't hurt either. This may sound odd to some, but I definitely did NOT want to be seeen as a Japanese national. I did my best to fit in, follow local customs, and whatnot, but never let it be thought for long that I was a local.