The Irish immigrants who came to America during the Irish Potato Famine and particularly those who came to Hell's Kitchen were predominantly Catholic because the poorest citizens in Ireland at the time were Catholics and the poor relied on the potato the most for their food. Hell's Kitchen up through the nineties before its gentrification was a working class Irish neighborhood (+Puerto Ricans but they came along a bit later). Foggy and Matt's families are both working class because Irish Catholics in particular in New York struggles to assimilate due to anti Irish and anti Catholic sentiment up until very recently. 'It's not every day a Nelson comes out of the land of hardware stores and cured meats." or something to that effect. Likewise Irish Catholics because of such strong prejudice would have been unwilling to convert - their churches got burned down etc. by Protestants which wouldn't exactly have given them the highest incentive to want to assimilate if they even would have been allowed. Added evidence includes his big family "the whole Nelson brood."

If he wasn't raised Catholic his family is probably secular. The people labeling him Jewish have not done their homework because unless he is a convert he would not be.

Sources below my iPad is being a pain in the ass and has erased this post like four times to my irritation.