In IglooDame's scenario, we are talking about a political union as a single country between two entities, one, the northern United States, larger and more populous, and the other, Canada, smaller and less populous. In this scenario, the northern states become the new demographic, political and cultural core of the resulting nation, with Canada becoming backwater provinces. Their political and social organizations also stay entirely intact, including their state level political parties, state NRA, etc, which become instantaneously larger and more powerful than any preexisting political parties in Canada - in a flash, "Canadian" politics realign around Democrats and Republicans being the two dominant parties, despite having little to no presence or support in the existing Canadian provinces.Note also that in this scenario, while these states lean Democrats, a lot of them have strong Republican - and MAGA/Trump minorities. It's not just people fleeing that political movement! They get added anyway, and suddenly "Canada" has more Trump supporters than Canadians living in it.
Materially, the only difference between political merger with the Northern States of America and political merger with the United States of America here is the ratios of Trumpians to no Trumpians. And maybe the location of the capital.
Which is wholly different from any gradual arrival of disorganized fleeing people, and merit no further comparison.