So my internet provider (for reasons out of my control) is the sort that requires you to log in to use the internet, kind of like at an airport for instance. The account I have with them has real ID on it. I know they can see that I'm using Tor if they wanted, could this compromise my anonymity in any significant way?
No, it cannot compromise your anonymity in any significant way. They will be able to see that you're using Tor. That's all that they'll see. Your situation is no different than anyone else's. For more details, check out my other comment in this thread.