That's normal to say "immigrant" if you're neither right-wing nor aiming to use it pejoratively. The blue-tribe pejorative for immigrant is "transplant".

It's pretty common, I'd say, in the zeitgeist. As an example here's a popular content creator (Conan was on his show): https://www.youtube.com/shorts/vQ6TOleoCTY

It's really not that different in use. A right-wing commentator might say "Immigrants need to assimilate and put down roots here, not just bring their own culture here" whereas a left-wing commentator might say (as you see in the above clip, paraphrased): "Transplants need to put down roots here and volunteer to join the community"