Personally I don't care if they're coming from Mexico or Sweden or anywhere else, I don't want people pouring in uncontrolled, no sane nation does. It has nothing to do with race, it's simple space and resources.
Seems like I hear that argument all the time, and despite my liberal tendencies I probably agree with you more than disagree.
This is definitely the situation in Finland, too. People who are trying to separate illegal immigration from legal immigration are slammed with "no person is illegal".
Currently, it takes over two months to get an residence permit even when you already have work in Finland. Instead of actually fixing that, the government is working on how illegal immigrants (especially people who have been denied refugee status in EU) can stay in Finland and live off social security.
Except that instead of talking about illegal immigrants or non-refugee status asylum seekers, they just use the term "immigrant", and claim that anybody opposing their immigration policy is therefore against all kinds of immigration, and thus inhumane and racist.
It does not help that whenever a statistic shows negative effects or things that do not fit the government agenda, the Finnish solution is to stop gathering and publishing that statistic.
I do not know how to have a logical discussion on this in Finland at all, because of all the semantic and social manipulation going on. I have "leftist" friends and lots of such acquintances (academic folks), and although their opinions on these matters does not make me "unfriend" them at all and I'm interested in exactly why they have the views they do, I definitely need to completely avoid these topics or I risk them "unfriending" me.
(Among those living off the social security themselves, you do see the opposite view, labeling anyone with a different ethnicity as an illegal immigrant only here for the social security and committing crimes. Good luck trying to talk them out of that, either.)