The far right are picking wedge issues not from principle, but from political expediency.

In the UK they've switched from attacking immigrants to attacking disability benefits, because the clampdown on immigration was effective (though they obviously are continuing to shout about immigration and immigrants).

So if the "open-door" immigration policy didn't exist, they would have picked something else as the wedge issue. They DGAF about immigration per se, it's just something that will rile up the base and get attention.