If we go by history, then it's still you being paranoic. In the US every half century has a particular group of immigrants they hate and fear. In the past it was the Irish. Now it's Mexicans. The US wasn't destroyed by the former, and won't be by the latter.
While I don't agree with him or care about cultures "dieing".... I would note that the Irish took like, a 3 month boat ride to get here and were from a very small country.
Where Mexico is literally within walking distance, and much larger and more populous.
A fully open immigration policy would be disasterous. Illegal Immigrants actually already to cost more money then they create. (Some do pay taxes because the IRS allows people to get tax numbers who are here illegally, cause... goverment is kinda greedy like that.)
Largely because they come here uneducated, often unable to speak the language and really, have zero future since you need a social security number to have any job of consequence or do anything really and uneducated people have a hard enough time having a future when being able to speak english and having a social security number.