Lately, Chick-fil-A has some high-profile fans. But an analysis from YouGov suggests that becoming a conservative cause is not good for the company’s brand.

The YouGov BrandIndex subtracts negative feedback from positive among its 1.7 million American fast-food eaters. Since July 19, when Chick-fil-A founder Dan Cathy suggested that changing the traditional definition of what constitutes a family is “inviting God’s judgment on our nation,” perception of the brand has dropped to 4 points below the national average from its spot at 19 points above the average before he made the comment.

(The only area of the country where perception of Chick-fil-A has not gone downhill: the Midwest.)

That drop comes as Republicans have rallied around the company as a conservative cause worth defending.

Former Arkansas governor Mike Huckabee declared Aug. 1 “Chick Fil-A Appreciation Day.” Former Pennsylvania senator Rick Santorum has live-tweeted his peach shakes. Speaking in Texas this past weekend, former Alaska governor Sarah Palin promised to stop by the chain on her way home (and then posted proof). Conservative activists touted long lines at various franchises.

Chick-fil-A has always been an openly Christian company, and the group’s past donations to anti-gay organizations were no secret. Some college campuses had already shunned the group.

But the national backlash against Cathy’s comments is far more widespread. The company felt compelled to release a Facebook statement affirming that Chick-fil-A policy is to “treat every person with honor, dignity and respect – regardless of their belief, race, creed, sexual orientation or gender.” Various franchise owners have been using the same statement.

When an aspiring politician says something controversial, the attention of prominent Republicans can be a career boon. For a fast food company, things are different. Have Democrats been fueling the fire with calls to boycott Chick-fil-A? Sure. But instead of joining a culture war, it looks like Republicans should back off and let Chick-fil-A do its own damage control.