Hey, guys. I've been playing D&D for quite some time, but I've just recently began moving toward more digital approaches. I'm hoping to put together a more complete compendium of races (including UA) in the homebrew section of this site. Is this against any rules?

If you are planning on publishing them, yes, it is against terms of service, as they only accept original content. If you just use them for your group's private purposes, then, no, it's fine. I don't know exactly how you are doing this, but I assume you are copy and pasting the content from the books you have bought into your own homebrew content. In which case, it's completely fine, as you have bought the books, and thus, have legal access to their contents. Even doing the same with Unearthed Arcana content is legal, because even if these contents are put into a paid expansion, they will probably be different than what you copied and pasted, as they go through a lot of changes during playtesting. 

So, yeah, if you publish them, it is ilegal. If you just use them by yourself, then it's fine.