seen your other post, Andyjg1234, did you have a nice time on eurostar? 
Op, can I ask some questions to clarify some bits?
You're fuming on behalf of your friend, you've put that your friend is upset, is this re the being asked to leave playgroup or the screaming or both?
If this playgroup wasn't linked to a church, would you have been as angry at this happening or not?
Your friend has been ignoring the screaming, so likely to other parents they aren't 'seeing' any action being taken, does your friend agree that this may have looked like what has happened to other parents at the playgroup?
Are you 100% sure / your friend 100% sure no one has tried to drop any gentle hints / suggestions /comments re her dc? Eg helper asking if they've had a busy morning (ie trying to hint is anything wrong that has caused dc to be upset?)
Has the number of parents dropped in any way that may be attributed to your friend's dc? (just asking as near us there would be 2 or 3 playgroups happening so you could take your pick as to which to , possibly parents have not been happy re the screaming and gone to a different playgroup?)
Are parents aware there are no special needs (as yet identified) with your friend's dc? If so, how? Has someone previously spoken to her to get this information? If so, what conversation has taken place re her dc?
It's a tricky one. It sounds like an informal turn up, cup of tea and chat group rather than a preschool arrangement where staff are responsible for the care of children. If so, it's likely the people running it aren't in a position to guide your friend or have the links that a nursery / sure start / health visitor have to locate or suggest extra support.
Def recommend getting hearing / speech checked out. How does her dcact in different environments/ with other people looking after her?