This is kind of a tough one and I don't believe there is really enough information in the X-Files universe to be able to answer this definitively. First of all, if I remember correctly, Mulder didn't know or even suspect that Kristen was a vampire in the scene you quote. If I remember right he knew that Kristen was basically part of a weird social circle that got off on pretending to be vampires and drank each other's blood as a sort of sexual fetish. So of course a natural question to ask such a person would be "aren't you concerned about AIDS?"
Next let's work through with the assumption that Mulder DOES know/think that Kristen is a vampire and he asks "aren't you afraid of AIDS?" It still seems like a perfectly normal and natural question to ask but maybe the intention of him asking was the same as the reason you asked. In other words imagine Mulder is asking...
Mulder: Aren't vampires concerned about AIDS?
Kristen's response doesn't quite answer the question of whether or not vampires can contract bloodborne diseases but it does indicate that they (or at least she) isn't concerned about them since they are immortal and can't die.
KRISTEN: I wish I could die.
So in summary, we don't really know if vampires are affected by bloodborne diseases but they certainly don't seem to be concerned about them.