If you use an online presence that is traceable across the internet, some subset of them will bother you everywhere or decide to make your life miserable when you ignore them. As such, anything that can remotely be seen as connected to you with any longevity is best put online without your name and with a throwaway nickname.
Given that precaution, nothing! Sadly a lot of people don't take this precaution.
If the code is released anonymously, what good is it though (in the context of research code)? Ideally it should be connected to the paper to allow for replication, and what academic would want to release a paper anonymously?
I think we agree then that releasing code connected to a paper is something I wouldn't recommend anyone actually do, even if I do like it when it does happen :)
Leaving aside the outright abusive, probably nothing. But how excited would you be to receive in your inbox "Your [beloved project] didn't solve my pet problem the way I wanted! This software sucks and the devs are lazy bastards who don't listen to the community". Then imagine getting one of these a month, a week, even a day if your project is very successful.
It's of course nothing like actual abuse or threats of violence but it's an emotional toll that I certainly wouldn't want to pay. I have better things to do with my life.