People hold factually wrong opinions all the time. What does it matter? It doesn't affect his ability to do his job. Similarly, her factually wrong belief does not necessarily mean that she is unable to perform her duties.
What we're talking about here is a disagreement in ethics. If I belong to an organization that believes stealing is wrong, but I think stealing is OK, should I automatically be expelled? No. Just because I believe it is OK to steal doesn't mean that I will steal.
Similarly if she belongs to an organization that holds that sexuality is not a choice, but she believes it is, it doesn't automatically mean she will treat homosexuals any differently. Especially when she makes no indication of treating them any differently.