Under moral relativism, you can accept that other people have different moral tastes, just as you can accept that other people have different tastes for food. But you cannot accept that such tastes are subject to normative assessment, making them 'right' or 'wrong' in any meaningful way.

So a moral relativist can say something like "I dislike your approval of female genital mutilation", but this is not a claim about the rightness or wrongness of the approval of female genital mutilation. It is instead a claim about their own sentiments. This is just like saying "Well I don't like sushi" in response to a friend saying that they like sushi. You'r not saying that them liking sushi is wrong.

I don't see why. A person's morality, even if completely subjective, is still one frame of reference under which actions, thoughts, etc can be judged. Therefore, it's perfectly possible to judge the approval of female genital mutilation as wrong - just as long as I realize that the judgment is subjective.

Or to put it in another way, meta-ethical moral relativism doesn't require normative relativism.

While we can distinguish between first-order moral relativism and metaethical relativism, it's widely accepted that the former implies the latter.

So it's not uncontroversial to say that you can be an objectivist moral relativist. In any case, this discussion has been about metaethical relativism.