robert borden, who was prime minister around world war one, campaigned on the slogan "a white canada" and succeeded in almost completely blocking non-white immigrants from entering the country until the pearson-trudeau government opened immigration policy. there were essentially no black, middle eastern or asian people in canada until about 1970; the country was something like 98% european. while the civil rights movement was happening in the united states, canada was an essentially homogeneous white society. this was strongest in the western part of the country, but was due to the fact that the tories were initially in control of the country almost continually up to world war two. this was a very british, conservative party ideology.
the nazis, on the other hand, aggressively prevented anybody that wasn't white from trying to migrate. if you were considered sufficiently european, you could come in and out of germany, but you could not leave germany if you were jewish, black, gypsy, slavic (they thought poles, czechs and ukrainians were "mongoloids") or gay, as you were under essential house arrest until you could be enslaved by the master race.
the nazis would have scoffed at the concept of expelling the inferior races, as it would mean that the gemans would be forced to work in the factories. conservatives, on the other hand, are in favour of keeping out immigrants precisely because they steal their jobs.
the nazis were weird and hard to understand using contemporary political ideas. they were a kind of vulgar marxist on some level, in the sense that they sought to use marxist ideology to advance the interests of an upper class, rather than the interests of a proletariat. they sought to use marxism against the marxists. being a communist, marxist, socialist or anarchist would get you sent to the work camps, partly because they'd call you a jew because they thought socialism was jewish. the nazis were actually kind of more like modern liberals, economically; it was a type of state capitalism. they were not very conservative in any sense of the term, except the most culturally narrowest, as inheritors of the prussian junker class system.
the nazis also loved islam because they saw it is a militaristic version of christianty and aligned with muslim groups to fight the british everywhere and anywhere. the purpose of what these people in the article are trying to do is reduce muslim migration to canada, but the nazis were actually in favour of muslim immigration and actually sought to build military and political alliances with muslims, often against christians, wherever they went. the nazis showed no aversion to arabs, turks, north africans or iranians, unless they were mistaken as jews.
these people are probably better described as trying to bring back the british empire than trying to bring back nazi europe and they may have some valid points to make, in that regard. if canadian law attempts to criminalize speech of this sort (it does not, in truth. that claim is false.), then the problem would be with canadian law, which would need to be corrected to allow for a more free exchange of ideas, but that isn;t actually the case. canadians should not be ashamed of their history or afraid to identify as who they are