“He’s trying to run an insurgent campaign as a millennial presidential candidate, but he’s doing exactly the same tactics of every president who has run before him: high-dollar campaign fund-raisers in Manhattan living rooms while saying he’s a blue-collar guy from the Midwest,” Mr. Westin said. “That just doesn’t square with us.”

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Mr. Westin, whose group also protested at a fund-raiser for Mr. Buttigieg on Tuesday on the Upper East Side, stressed that his organization had not endorsed a candidate for the Democratic nomination and said that the protests had not been conducted in coordination with the campaigns of any of Mr. Buttigieg’s rivals.

Sean Savett, a spokesman for Mr. Buttigieg’s campaign, said that it has received support from over 700,000 individual donors and that the average contribution in the third quarter was $32. The campaign did not directly comment on the protests themselves.

The brownstone that was the site of the Wednesday protest is the home of Kevin Ryan, an investor and entrepreneur who founded or co-founded companies including Business Insider and Gilt Groupe, and his wife, Pascaline Servan-Schreiber, a documentary film producer and business development executive. In 2012, Mr. Ryan hosted a Senate campaign fund-raiser at the residence for Ms. Warren.

Mr. Buttigieg’s decision this week to open up his fund-raisers to the press and disclose the name of his bundlers came amid a series of disclosures that also included the release of his client list from his time at the consulting firm McKinsey & Company.

As recently as Thursday morning, Mr. Buttigieg, whose work at McKinsey has drawn intense scrutiny, defended taking big-dollar donations, arguing that he would need to bring “everything we’ve got” to the fight to defeat President Trump.

Angst about Mr. Buttigieg’s move to the middle had led some former supporters to ask that their donations to his campaign be refunded. Twitter users have taken to using the hashtag #RefundPete, though an official with Mr. Buttigieg’s campaign cautioned that it has also been amplified by members of the far right. It is not clear how many donors have requested a refund, and the Buttigieg campaign declined to provide a number.