they won't change their position. If anything, their position will be radicalized. For example, from classical liberal to alt-right.
This is been a common sort of mantra since Trump won the presidency. Whenever we have a controversial event like this, people make a statement that any actions by those on the left will only further radicalize people in the other direction. I don't think it's true, but most of all, I don't think that other direction really leads anywhere useful. For the reasons I outlined previously.
Superficially at most. When you go to some of the most popular alt-right facebook pages, and you see caricatures of Jews and whole racial groups consistently disparaged and stereotyped, and when you see just how many people posting in them have cross-interests with white supremacist and misogynist movements, you realize that "welcoming" is a very, very narrow term.