This could be an easy answer, but I can't seem to figure it out.

I am the director of our church media and I run the broadcast during our live services. We have camera operators and our main camera (Canon XF405) changes white balance constantly even though the lights in the church aren't changing.

It often happens, when the camera op zooms in on someone (often happens on the outside singers where the lights aren't quite as bright). The image will start to look extremely warm and when we zoom back out, it will turn back to the correct color. It's odd and I have no idea if that's normal or what I should do

Don't use an automatic while balance, set it manually using a white card under the main light source for the flesh tones. You should find instructions in the camera manual.

Do the white balance for all the cameras with the card in the same position, so that they match.

That's what is so odd, I don't use auto white balance. I put all the cameras in the same white balance number, but it still changes sometimes

Page 77 of your camera manual says your camera may get better results if you use manual white balance for closeups. It gives no reason why. I would suggest doing that as an experiment. Point all the cameras at the same white balance card/board and manually WB them. Then practice a few zooms/closeups and see if there is a visual difference in any of the cameras. Any camera that shows a change may have an odd scene setting or internal filter set. I would also black balance all the cameras too.

If the location/sanctuary has external windows is the lighting changing due to sunlight, clouds, street lights etc.?

Also try the two preset WB settings - the should be fixed. Just pick the one close to your lighting sources.