Labor's candidate for Melbourne,Luke Creasey,also faced questions about his past social media comments as a Facebook post emerged where he appeared to suggest a lesbian couple end up sharing a single vagina.
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Labor is refusing to disendorse Mr Creasey who has already been forced to apologise for sharing a rape joke and pornographic material on his Facebook page in 2012.
Senator Birmingham said the Labor Party had"double standards"and called for Mr Creasey to be disendorsed.
Labor leader Bill Shorten and Victorian Premier Daniel Andrews both stood by Mr Creasey on Friday morning.
Mr Shorten said Mr Creasey's actions were"deeply offensive"and"shocking and stupid"but"he's come forward and said he was 22 at the time".
"He doesn't want to cause any embarrassment and he doesn't hold those views now. He has
apologised deeply and he certainly doesn't hold those views now,"Mr Shorten said.
Mr Andrews said Mr Creasey"shouldn't have said what was said,he shouldn't have posted,he shouldn't have associated himself with those views".
"That was wrong. The difference is he has owned it,he made an apology and I believe he is sincere."
On Monday,another Labor candidate,Wayne Kurnoth,was forced to quit the party over anti-Semitic social media posts and conspiracy theories including that the world is secretly controlled by an alien race of Jewish lizard shape-shifters,mythological beings able to change their physical forms at will.