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The boycott pledge was started by the conservative American Family Association (AFA).
"Target's policy is exactly how sexual predators get access to their victims," AFA President Tim Wildmon said in an open letter. "This means a man can simply say he 'feels like a woman today' and enter the women's restroom...even if young girls or women are already in there."
Wildmon urged people to sign the boycott pledge, claiming the policy "poses a danger to wives and daughters." He also urged people to complain about the policy on Target's Facebook page.
He suggested that Target should install separate unisex bathrooms instead of giving all genders access to facilities designated for women or men.
Target clarified its position on transgender bathrooms in a statement on Tuesday.
"We welcome transgender team members and guests to use the restroom or fitting room facility that corresponds with their gender identity," the retailer said in the statement. "Everyone deserves to feel like they belong. And you'll always be accepted, respected and welcomed at Target."
Target's statement included a redesigned version of its signature bullseye logo to include a rainbow.
Target Target redesigned its logo to include a rainbow.
"You have, again, shown that your stores are inclusive and meant to be a safe haven, and I intend to repay your loyalty with my own," one customer wrote on Target's Facebook page.
Another customer wrote, "I want to tell you that I will forever be a Target shopper." A third said, "Thank you for always being a place I have felt welcomed."
Not all the feedback was positive, however.
"I am appalled by your decision," wrote one customer. "Shame on you."
Dozens said they would never shop at Target again as a result of the policy.
"Shame on Target," one critic wrote. "Restrooms have placards depicting gender on them for a reason. I will not step foot in another Target."
Target is following in the footsteps of Kroger, which also recently clarified its policy on gender-specific bathrooms.
A Kroger in Athens, Georgia, posted a sign on its bathroom door saying: "We have a UNISEX bathroom because sometimes gender specific toilets put others into uncomfortable situations."
A customer snapped a photo of the sign and posted it to Facebook, where the post went viral.
Companies are starting to weigh in on transgender issues after the governor of North Carolina signed a bill in late March forcing people to use the bathroom that corresponds with the sex listed on their birth certificate.
In Minnesota, where Target is headquartered, a Republican state senator proposed a bill that would limit access to restrooms and dressing rooms based on individuals' "biological sex."