The claim that an ID is not required to vote in the NYC mayoral race is mostly true because registered voters who have previously voted do not need to show ID, although first-time voters or those who did not provide ID during registration must present identification.
They are not requiring an ID to vote in the NYC Mayoral Race.

Who Is Ahead in the NYC Mayoral Race? Latest 2025 Election Polls - The New York Times
Source: nytimes.com
Key Evidence
The NYC Board of Elections states no ID is needed for registered voters unless they did not provide it at registration.
vote.nycvote.nycVoter ID
NYC Votes confirms first-time voters must show ID if they did not submit it previously.
nycvotes.orgnycvotes.orgVoting Rights
Voters without ID can still vote using affidavit ballots.
pix11.compix11.comWhat do I need to bring to vote in NYC? Guide to voter ID
What the Evidence Shows
According to official NYC Board of Elections information and NYC Votes, registered voters generally do not need to show identification at the polls if they have voted before or provided ID when registering. However, first-time voters or those whose identity could not be verified by the Board of Elections are required to show valid ID either at registration or on Election Day.vote.nycvote.nycVoter ID
nycvotes.orgnycvotes.orgVoting Rights
Additionally, voters without ID on Election Day can still cast an affidavit ballot.pix11.compix11.comWhat do I need to bring to vote in NYC? Guide to voter ID This means that while most voters in the NYC mayoral election do not need to present an ID, there are specific exceptions primarily affecting first-time voters or those with incomplete registration information. No sources indicate a blanket requirement for all voters to show ID in this election.