Neoliberalism (a term which uses "liberal" in the global "economic liberal" sense and not in the backwards and confusing way we use the term "liberal" in North America) has been treated as a status quo viewpoint for a long time now in corporate-owned media, which many use to form their opinions. Its vanguards were people like Mulroney, Reagan, and Thatcher, all of whom forever changed their countries' politics, and all of whom were from conservative parties themselves.

Maybe mainstream conservatism up to the 1970s would have been incompatible with neoliberalism, but not from at least the 1980s onward. (Not saying there aren't the occasional socially conservative folks who might dislike neoliberal economic policies now, though. Just pointing out it is literally what most if not all conservative parties base their entire economic platform on.)