Is the camp a particular denomination itself? Or is it non-denominational?
If the camp itself is one denomination, I could see a problem because the vast majority of kids would be of that denomination. If it is non-denominational then you are going to have kids from all kinds of Christian churches which, it seems to me, would make there less chance of a problem.
Maybe you can find some reviews and such of the camp online that may give a little insight too.
Just a note, that non denominational does not always equal "safe". Or that it is inclusive of all religious beliefs. All it means is that the church/camp is not governed under a certain denomination and that they have created their own ways of interpreting scripture, liturgy, etc... One non denominational doctrine may be agreeable to you, while another may not. It's not so simple to say non denominational churches are open and welcoming and non judgemental.
I'll give an example. I live in Houston. 4th largest city in the nation and in the Bible Belt. Churches galore! I knew a family who drove an hour every Sunday to a non denominational church. It was a super small church. (Friend said there were maybe a dozen families). Why did they drive one hour to a super small church? Because according the family it was the only church that "interpreted the bible right." It was non denominational simply because it didn't fit in the doctrine of any known denomination. It wasn't inclusive...it was just its own distinct flavor of Christian.