So like... yes, this endangers same-sex marriage. It also endangers interracial marriage. It also endangers marriage for people who aren't Christian.
This is a blanket permission to be as bigoted as the clerk wants to be.
And if you don't think the fascists will push this as far as it will go, you haven't been paying attention.
https://www.advocate.com/politics/tennessee-marriage-licenses-officials-lgbtq#toggle-gdpr