Danny Boy or Molly Malone are not essentially part of the Catholic liturgy. Therefore,
they should require no religious deference or observance. (I don't have a deference or observance for them personally, regardless). The London Derriere is not essentially Irish. it's a manufactured pop tune from "Oirish" living in New York. Molly Malone is a lovely ballad, however.

To claim a fraudulent respect for a nebulous tradition in America is like saying that
one should genuflect before Mickey Mouse.

However, the Irish tradition of music is respectable and will continue to be vibrant. The plastic bowlers and green beer is the result of a hyped-up St. Pat's day in America.
The sensible Irish will not deify it.