When I was on the board of trustees at my church we created a policy that we would not post signs, but that open carry would not be permitted. Any usher or staff member is authorized to request that openly carried weapons be concealed or removed. That process is enforceable in Texas. We also had our police department present a class, open to anyone who wished to attend, on how to respond to an active shooter situation.
I know that some members carry every Sunday and as far as I know there have never been any objections. As previously mentioned, we’re fortunate to live in a gun friendly area.