No it isn't. The issue would be rather she has a right to deny others the operation of law because of her religious conviction. And the answer to that is no.many here already support same sex marriage
so
do you really care what they think?
the issue here is religious freedom
She can't deny black people medical treatment, even if she really, really believes they suffer justly under the mark of Cain. She can't deny Jews the right to live in her neighborhood, even if she really believes they're Christ killers and God's judgment follows them. And she can't deny homosexuals that same operation of law, no matter what she believes about them.