It all depends on where the push to have a children's religious service on Thursdays is coming from. If it is from the church, the pastor, the religious ed. director--then I'd say the church can do what it wants. The parents who attend the play session would have to decide if they wanted their children exposed to the religious service or not. This might mean that some parents choose not to attend.
But if the push for the religious service is coming from one mom, member of the church or not, then I think all the parents involved get to have a vote. The same way they would if one member, an equal among equals, wanted to change the group to a ballet lesson once a week, or to teach the kids how to read once a week, or anything else that is not part of the normal routine of the group. The idea can be floated, and all the members of the group get to vote.
Which isn't going to stop Religious Mom from going to the pastor and asking if she can hold an official children's religious service at the same time in the same place as the play group.
And in my neck of the woods, proselytize, evangelize and "sharing religion" all mean the same thing--someone trying to get you to convert to their religion. They are not interested in learning about other religions, just about getting more people involved in their religion, however unwilling their listener might be.