It seems, Doubting Thomas, that you have been aware of the religious sensibilities of (I assume) a majority of this organization's membership for quite some time, but have just now decided to "take them on" regarding their long standing tradition of holding a mass in conjunction with the event. Again, I am assuming your timing on this has to do with you being the event organizer this time around, which (again assuming) you have not been before, otherwise the issue would have come up for you before.
While I understand that the constitution may say non-denom, it doesn't mean that a mass can't be an official part of the event, or any other denomination's church and temple services. Now, I'm not Catholic, but I do understand the role Catholicism has played in the Irish immigrant community, including in keeping the music alive. I haven't got a problem with it at all, as I understand for many (especially older) musicians and their families, the music is as important as their religion, and vice versa.
While I have never been offended by the mass being a part of the events, I simply choose not to attend it, as most people who attend the event nowadays also choose not to do. If you are trying to appease the "dual tradition Protestants" you could always plan two services, one mass, one church service. And voila, you have dual traditions dueling on the day, and you'll have played right into the hands of those who wish to politicize the event along Northern Irish sectarian lines. Which seems like a very hurtful thing to do to the Catholic membership that has kept the organization going all these years. Sort of a slap in the face, that.
It also seems strange to me that, if you have been involved with this organization for any amount of time, that you wouldn't be aware of your fellow members sensitivities along these lines. I don't understand why you believe you should be able to do away with the long standing tradition of holding the mass. If it bothers you so much, perhaps it is you should find or found another organization more to your liking and your personal religious and political proclivities, rather than taking over someone else's and demand they change to suit you.