First things first...

A church is an easy mark for all sorts of violent scenarios.

You don't advertise a security team. For that matter, no one involved in regular church ops need even know there's a security force active within the church. You do need to abide by all the rules and laws governing such operations, including lawful concealed carry.

The security team should know unequivically who are and aren't members without the need for special ident.

If you want a deterrence, post a sign. If you want security, don't let anyone know what's going on that doesn't need to know, which means if they aren't part of the security ops, then they don't need to be told.

At our church, we probably have at least two different security teams. I am certain only members of the security teams are aware that people are in church armed and ready to respond to threats, and the pastor is not one of the people who knows. There are action/response plans and control points that dictate how the security teams will respond to various threat scenarios.