I think part of the problem here is many people posting to this thread don't know or understand how this organization works, what it's long standing traditions are, or how the organization has changed to accomodate newcomers down through the years.
The organization I am talking about is Comhaltas Ceoltóirí Eireann, which just celebrated it's 50th anniversary in 2000 or 2001. It is a fairly conservative (by religious standards, certainly) organization that was formed in conjunction with the Gaelic League (people who know Irish history will know what that organization was about, for those who don't, it was a very influential organization that has it's roots in Irish revivalism at the turn of the 20th century in particular) that promotes Irish traditional music and culture (including dance, singing, and instrument), the Irish language, and de facto promotes Catholicism.
Now, when I say this "non-denominational" organization promotes Catholicism, what I mean is, it has always included a Gaelic mass, usually with traditional music, as part of it's festivals. That is the Irish culture side of the organization. It is certainly not the only Irish arts and culture organization that does this. Catholicism is much older than Irish traditional music in Ireland BTW--can't remember who wrote that one, but it isn't pagan music at all. It is secular music, but to call it pagan denies the music's roots in Irish Catholic communities, and actually practiced an Irish Catholic folk religion hybrid, which incorporated some non-Catholic rituals and practices, just as Catholics around the world do. Ireland is in no way unique in that regard.
Now, there is a long standing feud of sorts between the Irish Catholic church, and Irish traditional musicians in Ireland. There is a ton of folklore about how the priest came into the ceili house and smashed up all the instruments, drove people from their crossroads dances, denounced them from the pulpit, etc. So some musicians harbor a good deal of animosity towards the hierarchy especially, as they were one of the conservative forces in Irish society in the post-partition days particularly, and were behind passage of the Dance Hall Act, and other prohibitionist types of legislation "for the good of the Catholic Gael".
Now, in Ireland, Comhaltas isn't that old of an organization, but it is the organization that controls the national and international competitions for Irish traditional music. Personally, I hate the bloody things, and don't think much of the organization itself, as it promotes competition, rather than the finer aspects of the music (ie the sense of joy, comradery, etc that comes with being part of a living traditional music community). The competitions are extremely fierce, and many a young, budding musician crushed under the weight of them. OTOH, many a fine budding musician with the stomach for the competitive scene does brilliantly at these things.
The organization's branches offer classes (including some which offer Irish language classes), concerts, and sessions, and the local competitions that feed into the larger ones. In the 50s when it was founded, this organization did more to keep Irish traditional music alive than any other organization. Some would also say, it nearly killed the music with the way it was organized, especially with the influence of the Catholic church. But people need to understand that the Catholic church's influence in Ireland in those days was incredibly pervasive. Nothing happened in the community without the priest being involved--especially when it was to do with youth. The local priest had a hand in music, scouting, school, you name it. And in some places in rural Ireland, this is still very much the case (usually much to the disgust of the local organizers).
So, while the organization has tremendous influence over the competition side of Irish traditional music, since the big Celtic music boom of the late 80s and 90s, Comhaltas' overall influence has waned considerably, because there is so much more on offer for Irish traditional music nowadays. Also, as a number of people have mentioned, the younger generation in Ireland, as everywhere else, aren't church goers, whether Protestant or Catholic, so they rarely or never attend the mass when there is one in conjunction with a Comhalatas festival.
Which leads me to what I believe is at the heart of the issue for Doubting Thomas--no one is required to attend the (often Gaelic) mass that is held on Sunday morning of the weekend of the festivals. No one. It is completely voluntary, and the tradition of the mass developed out of the tradition of holding Gaelic masses as a means of promoting the Gaelic language to the Catholic faithful (it's a "Faith of Our Fathers" sort of thing, as someone else mentioned above). The Catholics who cling to this not very old tradition, are usually very conservative types. They also have controlled the organization since it's inception. Now, as more local branches have formed in recent years, fewer and fewer of these conservative Catholic types have been in local leadership positions, especially as the rarely religious minded baby boomers started taking over in the North American branches. But the hierarchy of this organization at the national and international level is still pretty conservative.
So I gave my advice based upon my knowledge of this organization. Personally, I have never had anything much to do with the organization because I don't like the competitive nature of it, and I deplore the Catholic conservatism of the organization. But it is THEIR organization, not mine, to run however they wish. I would no more go in and start dictating that they aren't following their constitution because they hold a mass in conjunction with their festivals, than I would go into a wholly secular Irish traditional music organization with no affiliation with any religious communities, and tell them they have to start holding a Gaelic mass in order to be "authentic".
Comhaltas is a very particular sort of organization that will soon go the way of the dinosaur because it's conservative hierarchy is so out of touch with the mainstream. Every organization has a life cycle, and this one will either be completely reborn, or will eventually close it's doors because no one is coming through them anymore. I have no problem with that, because I know the music is healthier than it has ever been, and in no danger whatsover of extinction. The music has also managed to escape control by the Catholic church that once attempted to dominate it and dictate to the musicians, how NOT to play, when NOT to play, and where NOT to play. And has survived it quite successfully.
So, I don't buy into the scare tactics used by many that the music is dying. It is changing though. Now, some here are arguing that to fight the conservative patriarchs who run this organization, is to fight the good fight, and I just plain disagree with that. The reason I disagree with it is because I know why people want to fight for their own power base within the organization--just like this circumstance, there are always going to battles over who controls what the organization does, and who controls the organization's resources. That is what this fight that Doubting Thomas has taken on is essentially about. He thinks he ought to be able to put out the conservative Catholic majority in his branch (and the branches have a lot of power in this organization), and run the show his way.
Well, if he can take over his local branch, more power to him. But if he does it the way he appears to be doing it, he is going to alienate the very base of support within the local branch that the organization needs to survive on a local basis. Hence the dilemma of the Doubting Thomas.
I have No Doubt about what I think should be done. Do it their way this year, and if you so desire, work to bring change to the organization in future years. But as someone else said above, getting rid of the mass ain't gonna happen until this generation of men in control of the organization dies off, if ever. There are quite a number of committed Catholics who want to see the tradition of the mass continued.
Now, people can scream all they want that it is wrong for a non-denominational music and cultural organization to have religious services of it's community in conjunction with it's gatherings, but it is done in both indigenous and immigrant communities around the world all the time with traditional music. This isn't something unique to Irish Catholics, people. You find this sort of thing with many cultures' traditional music communities.
Now, the thing that makes the Irish a bit different (but not alone by any means) is the conflict between the Protestant Irish traditional music community, and the Catholic Irish traditional music community. But you see the same sorts of conflicts arise in areas where there is a long history of conflict between religous communities, such as in the Balkans.
Personally, I think it would be great if we just banned religion, and were done with damn manufactured "religious" conflicts. But I'm a bit more of a realist. It is their (Comhaltas) organization. They've been running the show with a mass (with a very few exceptions in the north of Ireland) since their inception. It is part and parcel of the ethos of the organization. If one is going to be a member, one needs to accept it, work with people to change certain aspects of the organization if you so desire, but also with the fore knowledge that you may not be able to change that which you are trying to change, and then it is your personal decision whether to stick with the organization, or strike out on your own with a new like minded group who share your sensibilities.
IMO, there is plenty of room in the world for a lot of different types of organizations promoting Irish traditional music. Live and let live.