Let's back up here....You mention that you moved. How recently? How far from your old home? Did your son have to change schools, or is he due to start school this fall in a new school other than the one where he'd been in kindergarten or first grade?
You mention that you changed churches (as a result of the move, maybe?).
I'm hearing change, change and, depending on whether your son changed schools as well, more change on top of change.
That's enough to throw the best-balanced kid a little off. If his fears were rooted only in visits with this one former neighbor family, you could figure that he was somehow scared after something happened with them. But his fears also extend to fearing the unknowns of the new church environment, new kids to deal with there, new adults in Sunday school to get to know, etc.
You also don't say how long you've been "moved away" from your old place or how much contact he has really had with these former neighbors since you moved. Yes, they played together every day when they were neighbors -- but if more than a few months have passed, well, you'd be amazed how just that short time feels like an eternity to a nearly-seven-year-old and he may now feel awkward.
But even if there's no issue with his feeling awkward and not wanting to stay with the old friends, it makes some sense he would be clingy with you for while. New house, new school coming up (maybe?), new church. He is having a lot of change in his life -- change he does not and cannot control. No matter how great he was before at bolting out the door, he knew then that he was coming back to his same home and church. Now he's not so sure. Again it would help to know if you moved a year ago, six months ago, three weeks ago....
I would not push him to do the camping trip. Please believe me, I'm a scout leader and when one is out camping in the woods, it is a nightmare for all involved, both adults and kids, if a child melts down in the night and has to be fetched home. I've stayed places where it wasn't even really possible for a parent to come get a child after dark because the area was down twisting, unlit roads. And even if the camping is planned for a well-lit family camping area right off the highway --you don't want him to endure the embarrassment and fright of being the kid whose mom has to come get him at 1 a.m. It's not worth pushing him to go; sure, he may miss a great time, but there are other great times ahead after he has gotten over this rough patch of dealing with change. He's got time on his side.
I'd let him forego the camping trip -- if it's not too late and he's not already gone. Meanwhile, I'd talk to the church leaders who work with the kids. Tell them what he said and ask them to talk to him one on one -- NOT telling him "Your mom said this..." because that will mortify him to death! But they can talk to him and ask if he has questions; ask what he most liked about his old church; ask what he'd most like to do in church; tell him about fun things they do for kids there; show him the cool facilities, etc. You can get to know parents of other kids at the church and see if you can get the kids to play together in the church playground if there is one, right after church one day, or before....Find ways to ease him in, rather than sending him alone to the children's church time without you there. He'll willingly do that once he warms up to the new kids.
Someone posted that he might have been abused or had a traumatic experience. That sounds pretty scary but from your post I doubt it. It sounds like a reaction to change to me, and I would not push it or scold him for being suddenly shy; ease him into things rather than pushing him into them just now. When you ask for reasons he honestly may not be able to articulate any reasons; he just may feel general fear of the unknown right now but I think it sounds normal. I would not necessarily think it's time for counseling unless it goes on and on or it becomes debilitating to his daily life.