The Scottish singer was even asked to provide proof of her sex before one show.
She recalls, "It did seem to cause some kind of furor and the more reactionary slab of the American population reacted, in some ways, with horror.
"I remember once they asked me to provide my passport to prove that I was a woman and not a man."
And she tells gay magazine The Advocate that wasn't the only gender issue the group had - she had to persuade bandmate Dave Stewart not to dress up like a woman.
She adds, "We had to stop Dave from getting into dresses... I had to say, `I'm going to be the one in the dress, dear.'"