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Less than four months ago, the staid Metropolitan Republican Club in Manhattan became an unlikely battleground between anti-fascism activists and a far-right group known as the Proud Boys.

After the Proud Boys’ founder, Gavin McInnes, spoke at the club, vandalism and violence ensued, as people associated with the group squared off with protesters on the streets of the Upper East Side.

Now the brawl has moved inside the century-old club. The fight mirrors broader tensions within the Republican Party around the country, pitting far-right conservatives energized by President Trump against a Republican establishment that was once a bastion of New York moderates like John V. Lindsay and Nelson A. Rockefeller.

The election for club president will be held Wednesday, and one of the two candidates, Ian Walsh Reilly, has won support from another right-wing provocateur, Milo Yiannopoulos, who posted a New Year’s Eve appeal on Facebook, urging his followers to join the club and vote for Mr. Reilly.