The reason? I'll let Ms. Mark-Viverto tell it in her own words: "The St. Patrick’s Parade should be a time when all New Yorkers can come together and march openly as who they are—but right now that is not the case for the LGBT community."
In other words, she is protesting the fact that LGBT people and organizations are not allowed to participate. This is a move even her openly-lesbian predecessor, Christine Quinn, did not make. One reason for that, I believe, is that Quinn was first and foremost an ally of then-Mayor Michael Bloomberg, who never would have boycotted the parade or encouraged anyone else to do so. On the other hand, Mark-Viverto not only has her own convictions but the support of current Mayor Bill De Blasio, who is also boycotting the parade in sympathy.
Of course, those who oppose the boycott are using the reactionary tactic du jour: Accusing those they are trying to exclude of being, well, exclusivist and bigoted. It's best summed up in a statement from the Catholic League's Bill Donohue:
"There is a growing contempt for tolerance and diversity in the homosexual community, and among their supporters, especially in New York... The protesters obviously loathe diversity: diversity means pluralism, a wholesale rejection of mandated, one-size-fits-all policies. What these activists want is the right to impose their agenda on Irish Catholics, neutering a day set aside to honor St. Patrick."
Excuse me...Who is trying to impose an "agenda" on whom? Who is trying to "neuter" what? I know of no LGBT person who is trying to impose his or her "agenda", whatever it may be, on anyone else. And, as someone who's marched in a few parades, I don't see how a desire to participate in the St. Patrick's Day procession is an attempt to "neuter" a celebration.
Say whatever else you will about De Blasio or Mark-Viverto, they actually seem to understand what diversity and inclusion are. Good for them!