SYDNEY (Reuters) - The first public campaigns ahead of Australia s vote on legalizing same-sex marriage have hit television screens, sparking a truth-in-advertising debate on an issue that threatens to destabilize the ruling center-right coalition.  Australians can take part in a non-binding postal ballot in September on whether to change the Marriage Act to allow same-sex couples to marry.  The process will inform the government on whether to pursue legislative change and join 24 other countries around the world where it is legal. The  no  and  yes  campaigns launched their first television adverts on Tuesday and Thursday, drawing immediate rebukes from their rivals. The  no  campaign linked same-sex marriage to paving the way for radical gender study program to be introduced in schools. Lyle Shelton, the head of the Australian Christian Lobby and spokesman for Coalition for Marriage, cited a case in Canada, and another in Britain.  Look at the UK where a Jewish school in London faced the prospect of closure because it won t teach radical LGBTIQ education,  he told Reuters in a phone interview, referring to the acronym for lesbian, gay, bisexual, transgender, intersex and queer/questioning people. Australia s Education Minister Simon Birmingham said the two issues were not linked while non-government organization Human Rights Watch (HRW) said the ad was factually inaccurate. Because the postal vote is not a formal election it is not subject to the same rules on political advertisements.  You can have posters and ads peddling outright lies,  said Elaine Pearson, Australian HRW director. Australian Marriage Equality responded on Thursday with an advert saying same-sex marriage would give young gay people the same dignity as everyone else. Spokeswoman Kerryn Phelps said gay and lesbian counseling services were inundated by people distressed that their lives and relationships had been put up for judgment.  It s humiliating and it s anxiety provoking,  Phelps said. The marriage debate has dogged Prime Minister Malcolm Turnbull for the past two years as he wrestles to sell the idea of a public vote to appease conservatives in his ruling government, many of whom only agreed to support Turnbull s leadership if he went ahead with the ballot. Conservatives expect any proposal to allow same-sex marriage would be rejected in a vote. The postal vote is subject to a High Court legal challenge to be resolved next week, with opponents of the process hoping it will be struck down before the issue is put to the people. 