If you're talking about the organisation I think you are, you may well find you have a battle on your hands here. Although the organisation is constitutionally non-denominational, I think you will find that the leadership of the organisation, who should be upholding its constitution, will not be neutral on this issue. If I'm doing anyone an injustice here I'm sorry, but I have a strong impression that there's a strong RC ethos in that organisation, regardless of what it says in the rule-book.

If I understand it correctly, no-one is suggesting that everyone must attend Mass, but they do want it to be part of the official activities at your fleadh (assuming we are talking about that particular organisation!) So the advice to make it optional isn't much good to you - if anybody is suggesting compulsory attendence I'd run 100 miles away from having anything to do with if I were you.

As regards who is pushing you into having this I assume it is the local membership who want this rather than being pushed by "the church". Your real dilemna seems to be whether to go with your principled views or the wishes of the membership (or enough of them to make it difficult for you if you don't).

I don't know the right answer here but here are a few suggestions :

Publish a list of local religious services in your program, including the major religious denominations in the area where the event is being held. If there is an arrangement that traditional music is being played at the mass, which I think is often the case, you might be able to highlight this somewhere in the program, but not in the timetable of official events.

Try to organise some sort of a multi-denominational service instead of a mass if this is feasible - something short with a bit of music could work well after which people could go to their own church or religious service, if they felt so inclined.

You may not get away with either of these, but its worth a chance.

In any event I don't think this is about the relationship between Irish Music and Religion, but about those within a particular organisation who would try to foist their wishes on everyone else.
Many, if not most, Irish Musicians continue to carry out their musical activities without reference to any particular organisation, and would not share the values that the organisation leadership espouse on many topics.

By the way, I personally think you are right - if some people want to organise a mass or any other form of worship then that is fine with me, but making it part of the official activities does conflict with the stated aims of the organisation.

I hope you can manage to find a way around this, but I wouldn't underestimate the degree of difficulty that is likely to be put in your way over this.