Sure, but there's a difference between a fear being tenuously plausible but overblown/stoked, and a fear being flatly incorrect and inverted. The former is harder to counter. The latter still has the standard problem of lies propagating faster than the truth, but it at least theoretically should be countered by the truth.

At least in theory, many people perpetuating this myth are at least nominally convinced that it must be obviously true, because the zero-sum thinking is simpler than the reality.

Of course, the other problem is people going "my anecdote beats your study", because they personally know someone who blames immigration for losing their job, and a study of people in general still lets someone go "ah, but that's not always true".

I also think that the main fear - at least where I live - is not job loss but national identity and crime. At least that's what the anti-immigration political messaging is about. I haven't seen the job loss argument in the decade I've lived here.

Facts are much lesd helpful here because half of the perceived problem is emotional.

1. Immigration to the U.S is very different than immigration to Europe in terms of outcome , and even immigration to Europe could be further disected; lots of differences if you come from MENA or come from Thailand

2. Not everything can be answered by gdp; there is a real issue of culture and values that could become eroded by huge influx of immigration causing societal strife.

The data in the UK says GDP goes up, GDP per capita and salaries go down (which is exactly what you'd expect to happen from first principles...).

So the trade is your country gets (sort of) richer overall and the elites get richer while the average person gets poorer.

If you're okay with that outcome, then yes no need to worry about the data!