For example, if you were to say that something is particular to only one race, you'd say the trait is "race-specific". So my question is, what is the opposite of this? I would say it's "race-inspecific", since that sounds correct to me and "race-unspecific" doesn't seem to make sense. Neither does "race-nonspecific".
Edit: I think the word I was looking for is "dependent" and "independent".