“Inclusivity is a core belief at Target,” the discount retailer said on its blog. “It’s something we celebrate. We stand for equality and equity, and strive to make our guests and team members feel accepted, respected and welcomed in our stores and workplaces every day.”

But the retailer, the third largest U.S. store chain with 2015 sales of $74 billion, was also taking a risk. However much Target attracts a progressive and middle class clientele, a retailer that size has to appeal to a broad swathe of society to reach that kind of sales volume. Including socially conservative customers.

Many such shoppers are speaking up, vowing to boycott Target over the policy. An online petition by the American Family Association calling for a boycott of Target stores has now been signed by more than 973,000 people (as of Thursday afternoon), up from 900,000 a day earlier, characterizing Target’s policy as a safety risk. “Target’s policy is exactly how sexual predators get access to their victims,” the AFA claimed, though it did not offer any empirical evidence of that. “Target should not allow men to enter the women’s restrooms and dressing rooms.”

That anger from opponents to Target’s policy spilled over to its Facebook page. “Incredible. I hope the lawsuit you get hit with the first time a child or women is watched while using the facilities brings a little damned common sense back to your company,” one customer wrote in response to an unrelated Target post about coconut curry soup. “Simply (sic) incredible that we women have NO say in who enters our restrooms while we are doing our business.” Her comment has garnered nearly 3,000 likes.

A Target spokeswoman told Fortune that the company would comply with all local laws but also said that “Our belief in and commitment to inclusivity has not changed.”

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Target is so far the only major retailer to have publicized its bathroom policy. (The New York Times reports that Barnes & Noble (BKS) and Saks Fifth Avenue parent Hudson’s Bay (HBC) have similar policies.)

And in doing so, Target has put itself squarely at the center of the biggest culture wars debate going right now. Last month, North Carolina passed a law restricting bathroom access to transgender people, prompting everyone from PayPal (PYPL) to rock star Bruce Springsteen to cancel various plans in the state.

There are many reasons Target would take a position on such a charge issue. It is consistent with its previous actions on LGTB issues, including featuring same-sex couples in its promotional materials. Target also is making a push for more affluent and more urban shoppers, which tend to skew progressive on social issues. And, as the retailer competes for the best tech talent for its e-commerce efforts in Silicon Valley, where major tech companies from Apple (AAPL) to Salesforce.com (CRM) have been at the forefront of the fight for LBGT rights, Target can ill afford to be seen not inclusive.

Indeed, those are pretty much the same reasons Walmart, (WMT) with its presumably more conservative customers, last year pressured Arkansas’ governor to veto a so-called “religious” freedom bill that opponents said would allow business to discriminate against LGBT people.

At the same time, given the current state of retail- Target’s comparable sales rose a hard-fought 2% last year – if those 1 million people indeed do boycott Target, it could be painful.

But it looks as though such campaigns rarely hurt a company. Target and Starbucks (SBUX) have in the past angered conservative shoppers with stands on LGBT rights and for asking shoppers to keep guns outside of their stores even when local laws allow it, and both companies’ sales continue to grow. Ditto Apple, Facebook (FB) and Google (GOOG).

So, the odds are, this will blow over.