"Stewart said D.J. Gainey gave him permission to send her a letter inviting the couple to visit his church."
If he had permission from her to send her an invitation to church, wouldn't it be even more inappropriate for her to seek legal action?
A man with a gun, and the power of the state asks "By the way, may I ....?" Not surprised they said yes. I am surprised that you don't see this as a problem. Look, I have no problem at all with him proselytizing ... but combining that with the official exercise of police powers is a REALLY, REALLY, REALLY Bad Idea (tm)!