If you’ve never been to the annual New York City St. Patrick’s Day Parade, better put it on your calendar for next year. That is, if there is a next year. Time could be running out on the world’s biggest celebration of all things Irish. Why? Because the parade’s organizers have for two decades steadfastly refused to allow gay and lesbian organizations to march under banners trumpeting their sexual orientation. The city’s self-appointed guardians of human rights long ago declared this policy exclusionary and intolerant. But, unlike in previous decades, the effort to paint the parade and its organizers...