It's not just a false assumption it's actually nasty. It is accusing anyone that is worried about this of only being so because now it's affecting Europeans, like concern on this issue is evidence of racism and previously holding a position of apathy wrt the treatment of people from elsewhere. It's a shitty argument and at best dismissive.
The other aspects of this like 'well duh, what did you think was going to happen' , 'suck it up, already happens to people from elsewhere' is a race to a very shitty bottom imo.
Europeans aren't being prized over those people from outside the EU who already have a fucking shit time and treatment in terms of freedom of movement/immigration policy etc. Surely it's about maintaining certain standards and rights so that those can continue to be opened up to others, not obliterating them and having to start from rock bottom again for everyone?
I think most people concerned about this were previously also concerned about the treatment of people from other parts of the world too, people tend to be consistent in their awareness and position on issues like these IME.
BTW
krtek a houby you are right, this thread is littered with 'both indirect and direct thicky' and 'racist' accusations.