At first I thought you were mistaken, but that's because I was remembering a different year.
According to this article, you're referring to 1991:
New York City Mayor David Dinkins passed on an offer to lead the St. Patrick's Day Parade in 1991, deciding rather to march with LGBT Irish people, who had initially been denied entry into the parade until Dinkins intervened. Nonetheless, that group was booed for the entire 40 blocks. People on the sidelines hurled epithets and even beer cans at them, which Dinkins dodged with an umbrella.
I think the deal was that members of the Irish Lesbian and Gay Organization (ILGO) could march but not under their own banner, which is why the article says that Dinkins was marching "with LGBT Irish people" rather than with a specific organization.
Another article states that this was a compromise (marching but no banner) that ILGO accepted for that year. That's when the beer was thrown.
What I remembered was 1992, when ILGO again wanted to march in the parade under an ILGO banner, and apparently was no longer willing to compromise. The parade organizer, the Ancient Order of Hibernians (AOH), refused to allow them. As a result, Dinkins became the first Mayor to refuse to march in the parade. He refused again in 1993, his last year in office.
He was succeeded by Giuliani and then Bloomberg, who both marched. It wasn't until de Blasio that NYC had another Mayor who stood up against bigotry by refusing to march in the AOH's exclusionary parade.
Incidentally, in a brief nod to DU's fascination with the 2016 race, I'll note that Hillary Clinton has a mixed record. From the first linked article:
In 2000, outgoing first lady and New York challenger for the U.S. Senate Hillary Clinton participated in the parade after months of debate. The following year, however, Senator Clinton marched in the Syracuse St. Patrick's Day Parade, where LGBT participants were welcome.
Back in NYC, there was some progress this year. Guinness withdrew its longtime sponsorship because of the exclusion. NBC, which had been broadcasting the parade, threatened to stop doing so if the AOH refused entry to Out@NBCUniversal, a group of LGBT employees of NBC. Faced with this threat, the AOH relented, and for the first time there was a banner-bearing LGBT contingent in the parade. (This is a little strange because the NBC group isn't specifically Irish, and ILGO would, objectively, have a better claim to inclusion, but it was the NBC group that had the clout with the AOH.)
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