Premier Will Hodgman has distanced himself from social media posts containing offensive material posted under Liberals Lyons candidate Jessica Whelan's name, stating this was a matter for the federal campaign team.
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Ms Whelan denied allegations she made a number of social media posts containing sexist and racist material and has called for an investigation into the comments, which she claimed must have been digitally altered.
Mr Hodgman was asked repeatedly in question time if he would dis-endorse Ms Whelan as the Liberals candidate for Lyons.
Labor deputy leader Michelle O'Byrne told the Parliament the comments were "deeply offensive, derogatory comments promoting violence against women".
"Ms Whelan is behind one post on the subject of feminism in America, which says, and I will quote 'Round them up Donald, cut their clitorises off and sell them to Muslims in Muslim countries, and cancel their passports, you'll make a mint', with an okay emoji," Ms O'Byrne said.
"How can you possibly stand by and not condemn this behaviour?"
Mr Hodgman said he was aware of the allegations against Ms Whelan and that she had denied making the social media posts.
"These comments, which as I say I've not heard before, are without doubt abhorrent," Mr Hodgman said.
"There is no doubt that those words, if used by any person, that they should not be endorsed as a candidate in this upcoming federal election."
Mr Hodgman said his government upholds its values to promote harmony and tolerance and firmly stands against any statements of this nature.
Opposition Leader Rebecca White said Ms Whelan should not continue as the endorsed Liberal candidate for Lyons.
"It is untenable to think that somebody that holds those extremist, racist views could represent our community," Ms White said.
Ms White said several of the comments in question were left on her professional Facebook page two years ago and were clearly made by Ms Whelan.
"Any claims that will be made by your party that this post was "digitally altered" cannot be based in any fact," Ms White said.
"They are not doctored. I am absolutely, 100 per cent sure, that those comments made by Jessica Whelan on my Facebook page are representative of a pattern of behaviour by her that demonstrates views that are intolerable."
Franklin Greens MHA Rosalie Woodruff said Mr Hodgman needed to address this matter because, as Liberal leader, he was one of the people responsible for approving all candidates standing in this federal election.
"Facebook posts bearing Ms Whelan's name have said hateful and Islamophobic comments including the statement that women who supported Islam should be mutilated and sold as slaves," Dr Woodruff said.
"As leader, you are responsible for setting the culture in the party and you can't flick this off as a matter for the federal campaign."
Ms Whelan was contacted for comment.