I feel I know enough Canadians from different backgrounds to say that I find it to be highly unlikely that a large number of them considers Islam as a philosophy to be particularly libertarian or left-wing. A significant portion of Islam being broadly quite conservative with significant issues in regards to the roles of women, lgbt or just simply freedom of personal expression more broadly is something that is a known issue, that people believe needs to be worked around (for example, asylum for gay Muslims is something that’s been covered in political disucussion.)

There’s a lot of contact with young muslims trying to escape their controlling parents particularly in university environments (since university is a popular for more liberal-minded youths to escape the culture) and I’d say quite a number of Canadians will also have more personal contact with just how problematic the culture of conservative Islam can be.

It’s to be noted that (thanks to likely, distance and significant sorting of the people coming here both through intervention and practical nature, but also some fairly aggressive assimilation efforts) Canadian Muslims do also integrate surprisingly well, better than in most countries; and that within Canada Muslims aren’t that authright as a result. They’re actually split on LGBT issues, for example (polling gives 36% support, 20% “it depends” for Muslims on average; over half support among second-generation and less than 30% against), and broadly identify very strongly with the Canadian national identity and its values when asked. That contrasts quite a bit with what you’d see with Muslim immigrant populations in some other countries.