In a different era, the dual statements that SoulCycle and Equinox Fitness posted on Twitter this week might have seemed radical: two popular American brands essentially disavowing a sitting president.

The statements were designed to distance the fitness chains from a fund-raiser on Friday for President Trump being held at the home of Stephen Ross, the chairman of the company that owns controlling stakes in Equinox and SoulCycle.

When word of the fund-raiser — and Mr. Ross’s connection to Equinox and SoulCycle, the indoor cycling studios it owns — became widely known, there was a furious reaction from customers. “We want you to know that Equinox and SoulCycle have nothing to do with the event and do not support it,” the Equinox statement said.

It was just the latest example of major brands edging away from Mr. Trump. But in an indication of how distasteful any connection to the president has become among some consumers, even those statements were not enough to stem the criticism.