With your birthday party, you have a say on who attends. I would just tell my dh that while you understand he is friends with Steve, you have no desire to be outside of their relationship and you do not want hm invited to your birthday party. My dh would totally understand this if this were us and vice versa.
As far as New Years Eve, let your dh invite who he chooses to invite. You will have plenty of other people there that you can talk to, etc. and if anyone would make a racist comment in my home, there would be a comment made. I think I would jsut look at them with this look, and say, "Wow. say Wow again, shake my head and walk away".