The petition is being driven by the American Family Association, a conservative organization that has a long history of involvement in American cultural battles.
Target announced last week it would "welcome transgender team members and guests to use the restroom or fitting-room facility that corresponds with their gender identity."
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On AFA's website, President Tim Wildmon said the boycott has resonated with consumers.
"Target's harmful policy poses a danger to women and children. Predators and voyeurs would take advantage of the policy to prey on those who are vulnerable. It's clear now that many customers agree. Target shoppers are leaving their allegiance to the store behind - and by the thousands every hour. No store can withstand that sort of loss."
Last year, Target announced it was moving away from gender-specific signs in its stores. For example, removing the use of pink or blue to guide parents in the children's sections.
"Inclusivity is a core belief at Target," the Minneapolis retailer said in a statement. "It's something we celebrate."
Are you boycotting Target over their transgender bathroom policy? https://t.co/cwAaIe8bKP— ABC11 EyewitnessNews (@ABC11_WTVD) April 26, 2016
Wildmon said the ball is in Target's court.
"As I have said, there is a common-sense and reasonable solution - a unisex option, which would cost Target money but would not alienate shoppers."
AFA said it is concerned about sexual predators taking advantage of well-meaning policies, a sentiment expressed by many who support North Carolina's House Bill 2.
"We want to make it very clear that AFA does not believe the transgender community poses this danger to the wider public," Wildmon writes. "Rather, this misguided and reckless policy provides a possible gateway for predators who are out there."
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