This is the kind of stuff I used to worry about before I started SSRIs. Now I can get off the train before I get to ridiculous things like world Amish domination.
The Amish lose a significant share of their children to secularism each epoch.
Climate change will force 1/3rd of the world's population out of Africa and into Europe/The Americas/South Asia within the next 30 years.
Unless you kill them at the border like the Saudi's are doing they will always still have incentive to get into your country by any means.
Only difference is you have the option to stop it.