“Her body type is minority” is a bit of a strange thing to say, like “minority” is a body type. From your explanation, you meant to say “Her body type is in the minority”, so I guess it was a misunderstanding.

Is the word minority so attached to race that it’s not used to talk about relative sizes in groups (if you understand what I mean)?

In that case I will not use it like that in the future, thank you for explaining!

Is the word minority so attached to race that it’s not used to talk about relative sizes in groups without clarification (if you understand what I mean)?

Yes, but it’s contextual. If someone is a minority, it’s usually referring to being a part of a minority class, often one that’s either protected or used by bigots as a point of hatred.

Being in the minority, however, can refer to having relative uniqueness.

English is hard. I’m sorry it has such stupid rules, but here we are.