Are there different standards for XLR cabling?
Yes. The XLR connectors has been used for a lot of different things. They were invented around 1950. In audio today it is mostly standardized, but vintage equipment may use the XLR connector in various ways. It was quite commonly used for connecting loudspeakers to power amplifiers.
Today it is almost exclusively balanced mic or line level audio. Pin 2 and 3 carry the balanced signal, ground on pin 1 is only connected to shield and does not carry any signal. [Edit: pin 1 has an important role when you use phantom powered mics, but that is a different question]
The church might have one of these: the Shure 545 could be wired for unbalanced connection. It is quite possible that the amplifier experts a high impedance mic with signal between pin 3 hot and pin 1 ground. If you connect a modern SM58, low impedance, balanced signal on pin 2 and pin 3, you will not get any sound.
If you want to use your modern mic, you will most probably need a Line Matching transformer, some examples shown here. I must be clear on that I am not sure exactly which one to use.
It would help if you could describe the make and model of amplifier, maybe even a picture.