I don't know whether I'd call myself anti-immigration, but I'm as left as they come and I don't think that being pro-immigration is a left/right value. You can be on the left and have objections to immigration, you can be on the right and welcome immigration.
I invite you to read the book [How Migration Really Works](https://goodreads.com/book/show/82005192-how-migration-reall...).
Most people think that being anti-immigration equals being racist and wanting refugees to be turned away. And given your comment, that is also what you seem to believe. However, the large majority of immigration is state-sanctioned (so work visas, etc.), is not the immigration you hear about in the news or that racists talk about, and it's neither a left nor a right issue.
Immigration does have economic benefits, but I'm certain you'll agree nothing in the world is only good or only bad. Immigration does lead to larger competition on housing (more people = more demand), and generally this happens in the cities where the housing crisis is the worst. So more immigration undoubtedly benefits landlords.
Immigration also means more competition for jobs, which leads in practice to lower wages. So it also benefits capital-owners.
So you can be leftist, campaign to increase intake of refugees, campaign against the housing crisis and wealth inequality, and be against immigration.
As an example that might change your opinion (beyond talking to a leftist who does not think immigration is nothing but good): when the Tories came to power after Brexit, they implemented policies that greatly facilitated immigration (2-4 times yearly intake to what it was before Brexit) [0]. Corporations and the right are very much pro-immigration. Would you have expected that?
[0]: https://en.wikipedia.org/wiki/Modern_immigration_to_the_Unit...