In 1972, when I was 11 years old, I watched my father march up Fifth Avenue in New York’s St. Patrick’s Day parade. He’s a Jewish guy from the Bronx, but he worked in city government. And on March 17, as the saying goes, everyone is Irish.

But the Irish disagree about what that means, and they always have. We need to keep that in mind as debate heats up over gay participation in St. Patrick’s Day parades, which have sparked controversy as well as pride for more than two centuries.

Boston’s parade organizers recently decided to admit a gay veterans’ group as well as Boston Pride, a large gay-rights organization. That prompted Marty Walsh — who boycotted the parade last year — to march in Boston’s St. Patrick’s Day parade, which was held on Sunday.

But New York Mayor Bill de Blasio, who likewise boycotted his city’s parade in 2014, probably won’t participate in New York’s parade on Tuesday. The parade has agreed to admit a delegation of gay employees from NBCUniversal, which televises the event.

That was enough for Guinness, which is returning as a sponsor, after boycotting last year, but not for de Blasio, who called the compromise “too small a change.” And it was too big of one for the Catholic League for Religious and Civil Rights, which announced that it would pull out of the New York parade unless a pro-life group could march under its own banner as well. ...