Court has claimed homosexuality has tarnished women's tennis and she has been vocal in her opposition to gay marriage, opinions which have put her offside with former WTA tour stars Martina Navratilova and Billie Jean King.
The issue has helped create a Facebook group, "Rainbow Flags Over Margaret Court Arena," which is urging spectators to display rainbow-coloured gay pride banners at the showcourt during the Australian Open which starts Monday.
Rennae Stubbs, an Australian who has won four Grand Slam doubles titles, said she supports activists who might show their support for gay rights at Margaret Court Arena.
"Margaret has said her feelings and it's public, and it has leverage," said Stubbs, who has been open about her homosexuality. "So I think this is the only way the people feel that they can be heard, through a sign of solidarity. As long as it (a protest) is done tastefully, that's the most important thing for me."
Court, 69, recently told local media in Perth, Western Australia, where she now lives that "politically correct education has masterfully escorted homosexuality out from behind closed doors, into the community openly and now is aggressively demanding marriage rights that are not theirs to take."
"The fact that the homosexual cry is, 'We can't help it, as we were born this way,' as the cause behind their own personal choice is cause for concern," added Court, who won her last Australian Open title in 1973.
Navratilova told TennisChannel.com that "seems to me a lot of people have evolved, as has the Bible. Unfortunately, Margaret Court has not ... her myopic view is truly frightening as well as damaging to the thousands of children already living in same-gender families."
Kerryn Phelps, former president of the Australian Medical Association and one of Australia's most influential gay spokeswomen, has called on the Victoria state government and Tennis Australia to drop Court's name from the 6,000-seat show court arena named in her honour.
"Time to rename Margaret Court Arena," Phelps tweeted this week.
Tennis Australia said in a statement that although it respects Court's playing record as "second to none ... her personal views are her own, and are definitely not shared by Tennis Australia."
"Like the WTA, we believe that everyone should be treated equally and fairly ... TA does not support any view that contravenes these basic human rights."