I think most of the people here gets it wrong.
A marxist doesn't promote immigration. We don't celebrate and promote immigration. That's why we are different from the "left" (i.e. SJW-tier liberals). We don't think that massive immigration (a different and more radical immigration than one guy acquiring a foreign citizenship or something like that) is good.
What we also won't do, and that's the difference we have with the populist right, is blaming immigrants for our economic or cultural decline.
tl;dr: we won't stand for any kind of reactionary IdPol, either in it's SJW variant or in it's right-wing populist variant.
Having said that, it's obvious that immigrants are here and they're workers and human beings just like us. That's why we offer them our solidarity and we would like to share the same struggle against capitalists (unfortunately, such struggle is practically absent in first-world politics today, instead it emerges in the disguised form of populism, the valve escape through which tensions temporarily alleviate but do not solve). We understand that immigration is an emergent phenomena of capitalism. When capitalist mode of production was introduced into the third world and the market dynamic became global, subsistence economies were erased and many of this countries became big crop farms with permanent unemployment for a lot of people. Unable to subsist farming their own land like many of these people used to do, obligated to search for a job to get a wage and survive, and unable to find it in countries that because of world division of labor became big farms, these people were first obligated to migrate from rural town to the cities. And that same movement, a dynamic that is inherent to capitalism, is reproducing nowadays from a country to another. That's why immigration is not something to be glad of. Hell no, I do not like. Even on a subjective level, I don't have absolutely anything in common with a migrant and the clash between his and my culture and subjectivity can be traumatic and violent for both.
But, what are we going to do? From the moment we understand the reasons why these people are obligated to migrate, we can't just hate them and blame them because it's the global dynamic of capitalism which pushes people to migrate, the same way it pushed our ancestors to migrate to a new continent.
Of course, a first and common-sense solution would be to aid these countries instead of sanctioning and invading them like the USA has been doing, right? But even if the USA hadn't destroyed many of these countries in central america, the dynamic I described would still stand because it's the product of a globalized market, and that's inherent to capitalism.
If you want to stop with massive immigration, which no doubt is traumatic for everyone, the only thing you can do is fighting global capitalism. That's why right wing populists are blind and dumb. They don't understand the deep causes, they don't want to understand them and they don't want to be responsible.