Funnily enough, the main objection by Christians was that Jesus was portrayed as being a grown man who dresses like a baby - but this was never in the musical - just the same actor playing different roles. I only realised this when I spoke to Stuart Lee, who wrote the musical, a couple of months ago.
As for whether the people on the 'real' show are genuine - I doubt all of them are. One of my friends made a few quid appearing on Trisha and Vanessa a few years ago playing different 'characters'. She roped in a male friend and pretended he was the father of her kids, cheating boyfriend etc. She got a few quid out of the TV shows for appearing, was put up in a nice London hotel for a night and got to practise her acting skills. And none of the TV researchers ever twigged she had appeared on other shows as other 'people'.