MrsLadywoman
We had these kinds of issues and tensions at our PTA too.
My advice would be to try not to think about it in terms of 'not offending muslims' as this leads to the kind of resentments and stand-offs you've talked about. The non-muslim PTA volunteers feel like they are bending over backward not to offend, the muslims feel like the PTA is run by a clique that has a bad attitude towards them and it spirals down in a bad way.
I would first think about what your PTA is for. People tend to think of it in terms of fundraising, but the truth is it is a hugely labour intensive way of raising funds. If you were really a fundraising machine you would just ask the well-off parents to donate £200 each and be done with it. PTAs are about fundraising, but also about bringing people together, creating a community, raising the school's reputation and profile in the community, having fun, making memories etc...
Things like printed towels and cards are ok, but they don't bring people together and they are quite expensive for parents compared to the money raised, because the company make most of the profit.
I bet if you asked your Head would s/he prefer you raised more money or did more to bring the school community together it would be the latter.
On this basis think about your events, and the way you run the PTA (timing of meetings etc..) in terms of whether it is inclusive to all the different families at your school -- WOHPs, SAHPs, People who don't work 9-5, Muslim and other minority religions, people with English as a second language, people with not much education, families with not much money, families with a lot of money (but not much time), new entrants, single parents, young parents, grand parents etc...
If you always have committee meetings in the evening, at someone's house with a bottle of wine not everyone will feel welcome and able to come. If you have them in the day WOHPs wont be able to make it.
It is a pain to do, but I think it is worth having meetings at different times, getting someone to translate if necessary and inviting people personally beyond the usual suspects, so it doesn't develop into the perception that 'we do all the work and no one else volunteers' vs 'the PTA is a clique of middle class white SAHMs' (this is my experience...it may not be the case at your school).
It doesn't mean every event has to be inclusive to everyone, but some (particularly the big iconic ones like the xmas/summer fair) should be. If you do a quiz night for example you have to recognise that only minority of parents who will feel comfortable coming to that - you have to be confident, educated and it helps if you drink alcohol.
In our school the Muslim parents were quite happy to come to, and volunteer at the xmas fair, carol concerts etc.... The things that worried them were events where drinking alcohol was a major part and events where their children might accidentally eat non-halal food.
While they would come to general family events, in general they wouldn't come to mixed events that were just for parents, since mixed sex socialising outside of the family is not part of their culture.
Positive stuff:
When invited one-to-one a lot of muslim dads joined the dads kickaround football team (but didn't go to the pub afterwards...)
One suggestion that came from some of the muslim mums was to have a 'women's pamper session' - they said to have it in the afternoon, at low cost rather than in the evening with alcohol and high prices. Some muslim mums did henna hand painting and eyebrow threading and we also got in masseurs and had a fruit bar. What was very successful about this event was that it was women only, so that nicab wearers took off their face veils which broke down some barriers between the muslim and non-muslim mums.
We also had a long and involved discussion about whether we could have a disco. The feedback from many muslims was 'if you call it a disco I wont be able to send my kids because MIL, GPs etc.. wouldn't approve'. We called it a summer party and had a children's DJ playing music and doing party games and almost everyone came.
I hope this is helpful, i am not suggesting these as rules of what-to-do and what-not-to-do but just my experience of how we managed to get over these tensions.