To some degree, this isn't a bad idea. For example, I abhor female genital mulitaliton (FGM) and I don't think it's particularly wrong to say that regardless of it being the "culture" of some people, it shouldn't be done.
If I weren't a moral nihilist, I certainly wouldn't be a moral relativist.
Cultural relativism is more useful in understanding why some people from different cultures behave the way they do, and examining if wither rejection of that behavior is based on a logical, beneficial value, or whether it’s based on the natural impulse to reject something foreign. Mistaken beliefs prevent cultural progress. Beliefs should be open to challenge.