Over the past year, a small troupe of drag performers with Down syndrome has taken the stage in London, Stockholm, Oslo and Montreal, adopting flashy alter egos and basking in the crowd’s applause. They call themselves Drag Syndrome.

The London-based troupe’s next stop was their United States debut: an art exhibition in Grand Rapids, Mich. But after the event was publicized this summer, there was a backlash from community members who were worried that the performers were being exploited.

That faction included Peter Meijer, a supermarket scion and Republican congressional candidate who owns the venue where the group was to appear. Last month, Mr. Meijer declined to host the performers , questioning whether they could give their “full and informed consent.”

On Thursday, the American Civil Liberties Union filed a complaint with the Michigan Department of Civil Rights against Mr. Meijer, claiming that he was discriminating against the performers because of their disability. The complaint also claimed discrimination on the basis of sex, considering they would be performing in drag.