No one said "everyone from their country is a bad influence." Indians were viewed as model immigrants in Canada for decades. Again, their good name is being tarred due to bad government policy.

My point is is that if leftists cannot talk about immigration policy in a nuanced way, right-wing extremists (for there are no other kinds of right wingers these days) will be the only game in town, and people who want to talk about immigration policy will therefore be drawn towards them.

Humans see patterns in everything, that's how we work. You can be a naive idealist all you want, but that doesn't change the fact that people will inevitably associate the effects of a bad policy with the policy itself.