They aren't denying Google and it's employees the right to move to Berlin, there's tons of areas in Berlin for tech companies to be, some tolerant of them, some actively trying to get more companies to move in. (and of course Google legally would have been free to move in despite the protests, but choose not to). That's needlessly over-the-top rhetoric for a localized protest.

This would go against the interests of the locals, that, frankly, in a community should come before the interests of some programmer that would find a job somewhere else.

It's complicated: if your freedom of movement harms somebody else, is it ethical? As an emigrant I can value the freedom of labour and movement but I can also see that this harms people if it becomes too extreme like in Berlin. That's why here lot of leftists are criticizing open borders and free immigration: mass migrations are a product of capitalism and we should solve the problem at the root, not just cope with the symptom.