"If you approve of womens rights, you should approve of Gay rights".

IMO we should have gay rights because gays want them, not because moral suasion was used successfully on people opposed to gay rights. Even if your argument above worked, I can't envision a plausible reasoning system in which the argument is valid. Can you offer one? Otherwise, it only worked because the listener was confused, and we're back to morality being a special case of psychology again.

Everything is a mixture of the invalid and the valid. Why throw somethin out instead of doing it better?

Because I don't know how to do moral arguments better. So far as I can tell, they always seems to wind up either being wrong, or not being moral arguments.