By Chris Hall, national affairs editor and host of The House

The Conservative Party's new deputy leader said Friday that Andrew Scheer has the right to not march in pride parades, and the party must make room for people like the Conservative leader who hold strong religious beliefs.

"I think that that's obviously his choice and we live in a country where that's his choice," Leona Alleslev said in an interview airing this morning on CBC Radio's The House. "Have we asked anybody if they marched in a St. Patrick's Day parade?"

Scheer's stance on social issues such as same-sex marriage is helping to drive a growing campaign inside the party to force him out as leader.

A number of prominent Conservatives have written opinion columns and appeared on CBC and other networks arguing that the party is woefully out of step with Canadians on an issue of basic human rights.

"This is a real deal-breaker for me, it's a deal-breaker for a lot of Conservatives," said Rachel Curran, who served as former prime minister Stephen Harper's policy director and now works at his consulting firm, Harper and Associates.

"There should be no equivocation around this," Curran told The House. "There is no room in the Conservative Party for anti-gay bigotry or for a view that same-sex marriage is somehow illegitimate or inferior to other unions, and that goes for childless marriage as well."

Scheer's most prominent detractors say they believe his clear discomfort with questions about his personal views on social issues during the campaign kept the issue alive, costing the party seats in Ontario and Quebec and, ultimately, the election.

Conservative deputy leader and Toronto-area MP Leona Alleslev defends Andrew Scheer's right to his own personal beliefs on same-sex marriage and tells host Chris Hall why she is a good choice for deputy leader. 7:48

Many say they've seen no change since then.

"The Conservative Party appears incapable of even offering table-stakes pleasantries to LGBTQ Canadians, while other cultural groups, be they religious, national or ethnic, command that respect without question," wrote key campaign organizers Melissa Lantsman and Jamie Ellerton in the Globe and Mail.

This week, two other prominent Conservatives, Kory Teneycke and Jeff Ballingall, launched an online campaign called Conservative Victory to push Scheer to step aside.

The campaign posted an anti-Scheer ad on Facebook on Wednesday. Ballingall told CBC News they're also planning to hire organizers and launch a social media campaign to put pressure on Scheer.

Scheer's opponents insist the Conservatives can't win the next election with him as leader. Alleslev disagrees.

"So the question is, do we not have room then for someone of a different faith or a different set of beliefs as prime minister?" she said. "Are we really sending a signal that there's no room for inclusion and tolerance at the most senior level?

Rachel Curran, a key advisor to former prime minister Stephen Harper, calls Conservative Leader Andrew Scheer's position on same-sex marriage a "dealbreaker" for her and other party supporters. 8:17

"I'm proud to be in a party that values and includes all perspectives. I think maybe he was uncomfortable. I can't speak for him, simply because his beliefs do have a place in Canada, just as much as everyone else's do."

Former conservative cabinet minister John Baird is putting the final touches on his review of the Conservative campaign. He was tasked with telling the party where it failed and what it can do to avoid another loss.

Conservatives went into the fall election insisting Justin Trudeau and the Liberals were vulnerable and that the prime minister's own missteps during the campaign — including his inability to recall just how many times he'd appeared in blackface when he was younger — offered a clearer path to victory for Scheer.

The sting of October's defeat is still being felt in Conservative circles.

Curran said she doesn't believe Scheer can change. She said his statements since the election on LGBTQ issues show he doesn't understand that many Canadians don't share his views, or that he recognizes his own views need to evolve.

"I think that's a real problem for a lot of Conservatives … and I think we need to make it clear that these are not views that the Conservative Party of Canada is going to accept going forward."

So the questions over Scheer's leadership will continue, as will the push to get him to leave before the party's April convention — where he will face a mandatory leadership review he could still win. And that outcome, his critics say, would ensure the party loses the next election, whenever it happens.