"Asylum seeker" is a specific term, for example see this UN glossary: https://www.unhcr.org/449267670.pdf. In particular it's not about huddled masses, it's about people escaping violent situations and active persecution. Putting "asylum seeker" in scare quotes and conflating it with general immigration is a right-wing thing to do. If you don't want people to mistake you for a right-wing partisan then consider just saying "immigration" of whatever type you mean.