This was my DS. He is turning 3 this week, but was nonverbal until age 2.5. He could sign as well. There was no way (still isn't) he is sitting in church. He is LOUD when he wants something. We are working on that but its hard to work on that during church and really, he is 3. He doesn't need to hear a full length sermon. When he is 4, he will do children's church.
He had major separation anxiety from BIRTH! My mom kept him while I work and he would go to no one but me, DH and her. I actually left the church that I was attending because I wanted either me or my mom to stay in the nursery with him to let him get used to it. They said I could but she couldn't. I got lectured by the children's pastor and the nursery director that he would never separate if I didn't drop him in the nursery and let him cry. I told them they were full of it and I quit .
So I found a new church. Explained the issue. Was told I could stay in the nursery and if my mom wanted to switch churches she could too. (She didn't quit.) After several months of me staying with him and going to the bathroom for short periods, I finally did it and left him for the whole hour. He did fine. Fussed a little the first time but since he was used to the room and the nursery workers he was ok.
So for me, what I looked for was flexibility and understanding of our specific needs, not some hard-nosed attitude and parenting advice. I get a text if he needs anything (very rare - one time I forgot his diaper bag and the worker asked me if I had any diapers - they ended up using some spare ones from the nursery closet.) I am on the nursery worker list now, we usually put in a veggie tales dvd or read bible based books. There are other non-bible based toys in the nursery which is fine too.