My own similar experience is that aged 5 is fine, but still worth asking if they have seen Punch before, aged 4 OK but ask more carefully if they have seen Punch before, and enquire if older kids will also be present.
I had an enquiry a year ago, from a German lady who seemed clear that she wanted a Punch show for her 3 year old boy, I advised her to wait a year, she said in Germany it was normal for 3 year olds to go to the puppet theatre. I suggested again wait and she said she'd talk it over with her husband. A few days later she insisted and confirmed she wanted to go ahead.
The show went well,but her 3 year old was totally silent and didn't really 'get it', but a two and a half year old girl really 'connected' and was answering to the puppets etc. The 3 teenagers and adults also enjoyed the show.
She thanked me saying that whilst "it was yes, fine", she was" a bit surprised at the, er, the violence." I explained that it was a traditional show etc, and she said that in Germany '...a puppet might be naughty and for instance steal a teapot."
So, on this occassion no real problems but they would have been better waiting a year.
Don't believe everything you think!