Hogshead-Makar, a retired gold-medal winning Olympic swimmer, said the belief that transgender female competitors would have an advantage in strength is still common among athletes
"But the medical experts say no," she said, "that there is a wide variance among women between height and strength."
The Women's Sports Foundation's position on transgender athletes is parallel to that of the IOC.
"If indeed they don't have this unfair advantage over people who were born female, then of course they should be allowed to compete," Hogshead-Makar said.
Lawless pointed to the sole transsexual golfer on the European Ladies Tour, whose ranking is not anywhere near the top.
"By past practice ... she should be the Tiger Woods of ladies golf," Lawless said.
At the college level, the NCAA has a policy that transgendered students are allowed to compete as whatever gender is listed on their state-issued documents, such as driver's licenses and voter registrations.
The issue of gender identity in sports made headlines last year, when South African women's runner Caster Semenya was forced to undergo testing after allegations surfaced that she had an intersex condition that gave her an unfair advantage over other female runners.
Earlier this year she was cleared by the International Association of Athletic Federations to compete in the women's division, though the results of the testing were not released for privacy reasons.
Hogshead-Makar said the closest comparison to the Lawless lawsuit might be the legal battle waged in 1970s by tennis player Renee Richards. Born a man, Richards sued for the right to play competitive tennis as a woman after being denied entry into the U.S. Open. The New York Supreme Court later ruled in her favor.