I don't think anyone decides that as such. Organizations and individuals decide who they do or don't want to associate with. If it turns out that very few people want to associate with you, then you've been ostracized. Your question is like asking "Who decides which people should be friends?", or "Who decides who should be popular?"

> Organizations and individuals decide who they do or don't want to associate with

No they don't, there are laws against that, for example you can't decide to ostracize black people from your company, you will get sued for that.

Hmm? There are laws against some forms of discrimination, but organizations have freedom of association just as individuals do. For example, political affiliation is not a protected class, so (in some states and some contexts) it is perfectly legal for a private company to decline to hire someone on the basis of their political views.

Thinking in terms of the US constitution and the laws built on top if it, ostracization by the government is forbidden and ostracization by private citizens and entities is not.

> ostracization by the government is forbidden and ostracization by private citizens and entities is not.

So its fine to fire all black people to ostracize them? No, of course not, so no you are wrong here, there are more limitations than that, people have rights protecting them from a lot of ostracism.

Yes, there are some narrow carve-outs, to encourage ostracization on the basis of behavior rather than the basis of identity.

This works because people can choose to not be jerks, but they can't choose to not be black.

And who would hold everyone in the group to that standard? How do you stop a lynch mob?

The police, that is how we stopped lynch mobs in the past.