> worry that that foreigners attempting to immigrate here for the long-term have a plan involving exercising influence on US politics from their position inside the country, in order to punish existing US citizens.

This is indeed a valid concern for immigrants like Elon Musk, Peter Thiel, and Rupert Murdoch. They’ve all had a significant deleterious effect on the US.

For the average immigrant just trying to live their life, it’sa much less valid concern. You could equally point the finger at the millions of natural-born US citizens who believe that the US is a “Christian nation”, who are well organized, and are trying to change the laws in that direction.