Non-partisan means that people of any party can belong.
There are Republicans out there who are interested in civil rights, regardless of their party's official position on civil rights.
They would be permitted to join, and welcomed.
If they would be kicked out of the Republican party for that, well, the Republican party is a partisan organization.
If the thought of belonging to a non-partisan organization whose goals are not shared by a partisan organization makes someone's head explode, perhaps the need is not to inflate the head, but to expand the mind.