The Reverend should tell any that request it that he does not perform civil marriage. Only Holy Matrimony, and that requires all the prerequisite counciling sessions and and church doctrine requirements. Much like Catholics require that a would be bride or groom must convert if they are not Catholic.
Unfortunately, all churches will have to start doing that. They may even have to separate from the state civil marriage all together, it might even come to not getting licenses . And people who want to make it legal would then have too have a civil marriage too, at a courthouse or JP. But the issue is staying with God and the Bible, and being married in the eyes of God, NOT the state. We can pray it doesn’t come to that, but it very well may.
Non-Catholics are no longer required to convert to Catholicism if they marry in the Church.
Clergy really ought not worry, at least not for the time being (except perhaps military chaplains.)
The law sees a significant difference between a clergyman performing a religious function and a florist arranging flowers or a photographer taking pictures. The former are protected by the Free Exercise Clause. The latter are not.
No they don't.
I'm Catholic and two of my kids are married to noncatholics.