Less than I would have if you had spoken about marriage rights.
The difference being that to deny a group voting rights, it means you have something against that group specifically.
Whereas for marriage, it could just be that your notion of marriage as a custom (how you think marriage should be) is incompatible with the group performing it.
If you found a minister of a non-specific religion who refused to marry to black two people just because he just didn't see marriage in his faith as something that happened between black people, how much faith would you have that he had nothing against black people, that it was just about he saw marriage?
Well, if his religion stated so, then I would have no reason to doubt him.
Religion can have any arbitrary rule. No marriage for X group. No priesthood for Y group. That doesn't necessarily mean that it also sees Y group in a specific light otherwise.
And what if members of his religion has mixed views on the subject?
This is part of the problem with it as a religious argument - most religions don't have a unified view of the subject. To bring it back to the matter at hand there are plenty of Christian's who have no problem with gay marriage so is it really a Christian view, or just a view held by some Christians (which is a somewhat different thing)?
Oh, and religion may have any arbitrary rule but that doesn't mean we have to accept it. There is more biblical justification for stoning than for homophobia yet we're not on side with stoning.
The difference being that to deny a group voting rights, it means you have something against that group specifically.
Whereas for marriage, it could just be that your notion of marriage as a custom (how you think marriage should be) is incompatible with the group performing it.