Maybe you're listening to other people but I don't see a popular case being made for immigration as a solution to world poverty.
There really isn't a policy of enabling mass immigration in to Europe. The point that everyone comes back to is Merkel's open invitation to Syrians in 2015, but they're ignoring that this was an exceptional, one-time response to a very specific situation and humanitarian crisis, and it was also a political mistake that cost her - she had to row back on it pretty quickly. The asylum seeker flow since then was significantly reduced. ("
Angela Merkel admits she lost control of refugee crisis in Germany and would 'turn back time' if she could - 'No one wants a repeat of last year's situation' " )
I agree people should be able to voice their concerns more freely without being labelled racists for example, as it just exacerbates the situation like you say.
It cuts both ways though, and people generalising about other people based on their (nominal) religion for example is always going to lead to silliness. (Funnily enough, there is the same group of people in Muslim countries making stupid generalisations about the 'Christian' west, as if it's a monoculture.)
This is what annoys me about things like Moz's Manchester statement. He implied 'Muslims' where he very well could have said 'Islamic extremists' for example. No-one was stopping him - there was no grand conspiracy against saying this.