Yes, its still possible, and I also wonder why NYC doesn't have a big nonpartisan primary, and then a top 2 runoff instead of a partisan general election like other cities do.
New York elections laws are geared to entrench political parties. Minor parties are able to stay on the ballot from year to year. From Ballotpedia:
In New York, a political party is defined as any political organization whose candidate for governor or president at the last preceding election polled at least 130,000 votes, or 2 percent of all votes cast for the office, whichever is greater. New York does not provide a process for political organizations to gain qualified status in advance of an election. Instead, political organizations seeking party status must run a candidate for governor or president via the independent nomination process (see this article for more information). The organization may denote its name on the nominating petition; the organization's name will then appear alongside the candidate's name on the ballot. The name selected must be rendered in English and cannot suggest similarity to an existing party or a political organization that has already filed. If at the general election the organization's candidate for meets the aforementioned threshold, the organization will then be recognized by the state as a political party.[1][2][3]
Right now, there are 4 permanent political parties: Democratic, Republican, Conservative, Working Families. In New York, under certain conditions (usually the chairman of a party signing a Wilson-Pekula waiver), a candidate can run as the candidate of two (2) parties and appear twice on the ballot, when the votes a candidate gets on each ballot line will be credited to that candidate.
Rudy Giuliani won in 1993 with lots of support from Democratic pols; he was the candidate of the Republican and LIBERAL (yes, LIBERAL) parties, and he had those endorsements in 1997. Michael Bloomberg left the GOP after 2007, but the GOP signed the necessary waiver for him to run on the GOP line for a third time.
Giuliani and Bloomberg were not "Republicans". They were "Not Democrats". John Lindsay was a Republican who was elected in 1965 as the Republican and Liberal party candidate which is why he carried Harlem and Bedford Stuyvesant. Lindsay lost the GOP primary in 1969 but was elected as the Liberal Party nominee against conservative Republican John Marchi and conservative Democrat Mario Procaccino.
New York City has changed demographically. Roughly 15% of its residents are Asian; this is a huge demographic change. Only 32% are White/non-Hispanic. 29% are Hispanic (7% white Hispanic) and 23.5% are black. This demographic mix makes the city less likely to vote for a Republican unless (A) the Republican candidate is a prominent Democrat running with the Republican endorsement and (B) the candidate was of an ethnic group somewhat ignored by the Democratic establishment. (If NYC elects an Asian Mayor, it would likely be a Democrat given the Republican nomination and there would likely be a Democratic split with a third candidate running on the Working Families line.
One reason this scenario is less likely now is the weakness of the NY State GOP. Despite gains in 2022, the NY GOP is clearly a minority party, with little chance of retaking the State Senate. (The Assembly has been hopelessly out of reach since 1975.) The "Fusion" concept was a concept pushed by Republicans of the 1950s and ramped up once Nelson Rockefeller became Governor; it has become passe' since the eclipse of the NYS GOP statewide. So while the Republican candidate has won 7 of the last 14 NYC Mayoral elections, the winner hasn't always been a registered Republican, and in one case, the Republican didn't have the GOP nomination and needed a 3rd party cross-endorsement. A GOP Mayor for NYC is much less likely than it has been not that long ago.
