Her 1989 song "Like A Prayer," with links between religion and eroticism, caused Pepsi-Cola to cancel a sponsorship deal.
In 1992, she released a book called "Sex" with nude pictures of the star that caused a media sensation, and in 2003 her same-sex kiss with Britney Spears at MTV's Video Music Awards proved to be yet another celebrity news firestorm.
While Thompson noted that Madonna has successfully boosted her career in the past with controversy, he added that celebrities should speak their minds if they want.
"The whole notion of a democratic republic is that this wasn't just about politicians, that anyone could shoot their mouth off about whatever they wanted to," Thompson said.
But David Horowitz, a conservative writer and activist, took a more dim view of Madonna's latest controversy.
"We're in a sad situation if we're turning to entertainers for political wisdom," he told Reuters.