I heard inspecific is not a correct English word, but I find in some circumstances it makes more sense than alternatives

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".

I think usually, using your example, you would say 'non-specific to race', 'independent of race', or maybe 'race-independent' (although the last one doesn't sound quite right).

Perhaps use 'non-race-specific'?