The liberals would be aghast at Baptist volunteers. They would be afraid of violating separation of church and state and all that. Plus, odds are these Baptist people oppose homosexual marriage, so the liberals would reject aid from such people.
Well, they’re there. Maybe the locals be more aghast at how badly their purported government saviors have responded and will be more receptive to a Christian message as a result.
Let them....
Then they'll die off. It's a win/win situation.