That's a common misconception. Churches simply are not required to perform marriages. They can, for example, refuse to marry interracial couples if it goes against their beliefs. And they can certainly choose not to marry people of other faiths, even though that goes against religious discrimination laws.So...no, no, no.
It's not a matter of if they are required to perform marriages or not. It's a matter of being discriminatory when they are being officiates of the state in regard to a state function, marriage solemnization.
Churches should be sued and not allowed to discriminate when they are functioning as an officiate of the state. I know people think it can't happen but it will because it's a violation of principle in regard to state anti-discrimination laws. It's just that right now people are tolerating this kind of transgression, the same way blocking gay marriage was tolerated, or interracial marriages, or women voting, or interfaith marriages, discrimination in housing/employment/work, etc.
The way to solve it is for the state/government to not recognize religious leaders and institutions in regard to the solemnizing of state recognized marriages. That's not being anti-religion or church at all, in fact it is protecting it because it is taking religion out of the matters of state so they, for example, won't have problems like this.
Either churches will have to solemnize any marriage that is recognized by the state OR they will be removed as people/groups that can be officiates of the state in that regard. I think the latter option is the right one.