There is a tendency to fall into a 'us and them' mentality when people take these distinctions too seriously Not everyone or every group falls into this trap, but it does happen. And this occurs even if the group conists of a variety of supportive people from 'mainstream' categoies, its concept tends to be viewing through the lens of categories (even if done for good intentions). Hence, the categories remain. Unfortunately (at least in political contexts) people see the categories first before the underlying issues, and plenty of people (on all sides of the issues) manipulate those perceptions.

Of course the principle of free association allows anyone to form a group for whatever reason they want, but you will never eliminated discrimination by codifying it.