But in an interview Thursday the Tory leader flatly rejected the assertions and said he supports abortion rights and same-sex marriage — his position on the latter having changed.
"Times have changed. Positions have evolved," Pallister said in an interview with The Canadian Press. "The decision that was made by the House of Commons (on the definition of marriage) is the decision. And I accept that decision."
Pallister has come under increasing attack from some of the candidates running for the NDP leadership. The party has sunk in opinion polls since raising the provincial sales tax in 2013 and Premier Greg Selinger has been facing a caucus revolt led by senior former cabinet ministers including Theresa Oswald.
Oswald, who is running to oust Selinger in a March 8 leadership vote, said her rebellion was prompted largely by a desire to revive the party in time for next year's election and to prevent Pallister from forming a government that she said would be "anti-gay, anti-women."
Oswald and other New Democrats have pointed to Pallister's comments when he was a member of Parliament in 2005. In a Commons debate on same-sex marriage, Pallister called the idea a social experiment that would abolish the "societal norm" of children being loved by a mother and father.
Pallister said Thursday there were politicians from all parties who opposed same-sex marriage at the time. He also pointed to media reports from 1987 involving former Manitoba NDP premier and governor general Ed Schreyer — then Canada's high commissioner to Australia —who called homosexuality "an affliction."
So has Pallister's personal position evolved?
"Over time, sure it has. And, I mean, the fact is the decision's been made. The fact is what we all want to see is loving relationships supporting — when desired — children, and we want to see strong families."
The renewed focus on Pallister has been prompted in part by the recent nomination of James Teitsma as the Tory candidate in next year's election. Until recently, Teitsma was a board member of the Association for Reformed Political Action, a group that aims to bring Reformed Christian beliefs into the political arena and which has fought same-sex marriage and abortion.
Also, federal Conservative MP Rod Bruinooge, a high-profile anti-abortion advocate within the party, announced earlier this week he will not run in the next federal election and left the door open to joining the Manitoba Tories.
Pallister said if he were premier, he would not attempt to impose any restrictions on abortion or same-sex marriage rights.
"No. No. No. That's not on the radar and it's not in our planning," he said.
He was asked if he now personally supports same-sex marriage and abortion rights as they exist.
"Yeah, on both. And yes, I also support the process by which those decisions were debated and dealt with. And that's important to understand. Parliament had the opportunity to debate the issues. They debated them. They're dealt with, and to my satisfaction."
Pallister accused Oswald and other New Democrats of trying to deflect attention from the NDP leadership turmoil and economic problems facing the province.
"To make hypothetical assertions as the NDP does, well, I could assert something for you. Why don't I assert that the NDP is going to raise taxes again if they get another chance?
"In all seriousness, I've got facts on my side. The NDP has phoney (assertions)."
The NDP shows no sign of letting up.
Steve Ashton, a former transportation minister who has joined the leadership race, said Thursday he would not believe anyone who says Pallister has modern social views.
"His economic policies are from the 1990s and his social policies are from the 1890s."
One issue on which Pallister's position has not changed is an anti-bullying law passed in 2013 that requires schools to accommodate students that want to establish gay-straight alliances.
The Tories opposed the law on a number of grounds, including a fear that it might infringe on the rights of religious schools that oppose homosexuality, and wanted it referred to the Manitoba Court of Appeal.
"That was a thoughtful amendment ... because what that would do is ensure that the legislation had the force of law," Pallister said.
So would a Tory government change the law?
"No. It's not been on our radar."
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