If you hold a public office, yes. You cannot use the public office to enforce your religious convictions. She has every right to believe same-sex marriage is wrong, but she can't use her position in office to enforce that belief and infringe on the rights of others. If she cannot do her job because of her religious convictions, then she needs to leave that position. Just as I cannot deny someone service because I believe their religious is wrong, I cannot be denied service in the public office because of someone else's beliefs. It's totally OK for someone to discriminate against LGBT people because their religion says so, but it's totally not OK when the LGBT community finally fights back. If I denied someone service because they are Christian, that would be wrong. But it's totally OK to deny someone service because they're gay, right? My religion said so!