1) there is a changing table in the men's room in every church of which I'm aware, and it's usually in a multiple-use bathroom

2) if the changing table is occupied, just wait the minute or 2 until the other dad has finished

3) please, never, ever change a diaper on the counter in the kitchen

4) every bathroom that I've seen has a trash can in it. Throw the diaper in there. If you think it's too stinky to sit in that trash, it's probably also too stinky to be in any other trash, including one in a hypothetical father's room. In that case, walk with your kid out to the dumpster. No big deal.

5) a mother's room exists in many (most?) buildings so mothers can have privacy if they need to nurse. Fathers (even in 2022) don't have that need. Changing a diaper works fine on the existing changing table.

6) church building room space is at a premium. Designating a whole room just for fathers to occasionally change a diaper, then leave said diaper in there to molder away doesn't seem like a good use of funds.