Hey Doubting Thomas. I'm not a member either, but an interested regular viewer of the forum. Here's my tuppenceworth.
Re. the role of the Church in the past. I would argue that the Church has not been supportive of Irish culture, quite the opposite. In political terms, the church has historically supported British rule (the status quo), excommunicating IRA members, etc. This was church practice from as early as 1179AD. Culturally speaking, the church in the C20th was very anti-music and dancing, and one of the reasons why traditional music and song was in such poor shape in the mid C20th. (puritanical so and so's, rather than ideological opposition, methinks).
Second, I don't know what your organisation is, but if it is constitutionally non-denominational, it really must be kept that way. I'd blow the whistle to anyone investing money and let them know the plans for a mass, if it's to go ahead - seriously the church can be incredibly insidious and it tarnishes the image of Irish music that we all should aim to promote. It's essential to lose the catholic tag from Irish music and make it accessible to all. This politicisation is a relatively recent phenomenon. 2 generations ago, the music belonged to all the people, whoever wanted it. There is a difference between religion and politics. Let the politically minded steer clear if they wish, but protestant children should be brought up knowing that it is equally a part of their culture, not the preserve of the catholics. Music should be non-political and all embracing. While Loyalists will tell their children that it's not for them (which is disgraceful), the fact of the Catholic church insisting upon a Mass at a fleadh is an equally sinister act, re-inforcing stereotypes and excluding people who have a right to their share of the tradition. Be strong. peace and love, a.w.