Sure, she's not really standing in the way of people getting their marriage licenses. But there's something to be said for not using an official government position as a platform to preach your personal beliefs. It's one thing if you're in a political position (Congress, state legislature, etc)...but using a non-political government office to push some personal agenda seems wrong to me. If she wants to, as a private citizen, protest about how gays are ruining America, that's her right. But that's NOT her job as town clerk.
I tend to agree. I see this as no different than Muslims working at grocery stores but refusing to sell or bag pork or liquor; if your religion prevents you from doing some part of your job, you need to find another job. If you really believe G-d is not okay with you issuing gay marriage licenses, why the hell would He be okay with you delegating that to someone else? Put on your big girl panties and resign.
And at the very, very least, shut the hell up about it. We all have laws we don't like; if we went around making an issue of them like prima donnas, we'd never get anything done except pissing each other off. Maybe the tax assessor doesn't believe churches should be exempt from taxes; should he/she be making an issue of that?
To quote Laura Ingraham, shut up and sing (or do whatever is your job.)
And for the record, I have no problem with her views. I just have a problem with her letting them affect her responsibilities. Should it be all right for her to tell a gay couple "I'm sorry, you'll have to come back when my deputy is here, because I don't approve of your lifestyle"? Hell no. We wouldn't accept that if her problem was with interracial couples or fat people, and we shouldn't accept it with gays.