Hi Nicole,
I don't think you're being overprotective, but then maybe I was overprotective with my kids, too -(lol!)
I guess in this situation I would say no to the playdate unless I could find a way to get to know the parents better and visit their home first. You could find an excuse to have your daughter come home from school first (check on homework assignments before playing, a chore that needs to be done, etc) and then take her to their home and go with her to the door and wait to be invited in.
Like someone else suggested you could bring some snacks to carry in. Then you could stay to visit with the mom for awhile or the whole time if you felt uncomfortable about anything.
Just because they are Christian doesn't mean their home would be an acceptable place for my child to visit without me. I had some "Christian" neighbors who were very physically and mentally abusive to their children so I didn't allow my kids to visit at their house without me.
To avoid a similar situation in the future, when your daughter wants to invite someone over for a play date and you don't know the parents you could call the mom and extend the invitation to come over with her child for the first playdate to visit and get acquainted. At that time you could tell her that you understand that she (like you) would want to get to know people first before letting her child come over alone.
If that is too direct, you could word it more friendly like "as long as our girls seem to enjoy each other's company so much, I thought we should get acquainted, too".
If that doesn't work, you could take the next step to be more direct and say
"I'm planning that you'll want to come in and visit for at least a few minutes when you bring her over to have a chance to get to know each other a little better."