Newman, whose daughter is transgender, spoke in favor of the bill banning discrimination against LGBTQ Americans.
Greene tried to block the bill, so Newman put a transgender pride flag outside Greene's office, "so that she can look at it every time she opens her door," she said on Twitter.
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Greene responded by putting a sign up outside Newman's office, which says "There are only two genders."
Illinois Rep. Adam Kinzinger asked his fellow Republican to stop her attacks. In a tweet he said "This garbage must end."