At my church, groups can use the facilities. These groups do not have to be religious in nature.
We have AA type meetings, Aerobics, SAT study, etc.
If the group is for a member then I believe the cost is lower.
Anyway, you thought you were joining a local playgroup that happens to meet at the church, not a religiously affiliated one.
If you want to take your child to church, you could do that on Sundays and have them go to Sunday school.
If they insist on having a religious service, then that is going to cause you to leave. I can't imagine they would think that a good thing!
I would talk to the leader and say "I joined this playgroup because it had kids my kid's age that were from the local area. I get my spiritual needs met elsewhere (your bed on a Sunday morning, another church, another religion, etc) so am not looking for a religious service. If you all would like to add a service after playgroup that would be fine for those who are interested. Let's leave the playgroup the way it is."