I think calling for the professors dismissal in this instance is completely unwarranted. Not only do we have only one side of the story here, we don't even know what those tweets were, or if there's anything else at play here, nor is the relationship very clear here (the supposed student was actually studying in china for 3 years? What exactly was the relationship with the Swiss professor then?) Additionally, it's just not acceptable to demand others suffer the consequences for fights you picked, no matter the justification.
I mean, there is clearly an argument that the funding, influence and prestige the Confucius institute grants also allows them influence, and that that influence is perhaps unwanted. But if that's the conclusion, we should demand a counter-pressure by parties that are better able to withstand chinese pressure, e.g. perhaps some coalition of European countries that reject the institute whole cloth. Unfortunately, I doubt the EU can do much here because it's already been infiltrated by governments that clearly appear to be under Chinese influence, such as Hungary, and it needs unanimity for most action; and of course Switzerland isn't even in the EU.
To put it another way: I have doubts a country like Switzerland would dare to pick this fight with China alone - but if so, how absurdly unreasonable is it to expect an individual professor to, without any kind of policy. The whole issue puts the wisdom of Switzerland's idea of independence at risk.
Also, I no matter how you reject China's actions, I think it's morally pretty questionable to put your partner's family at risk, even if you think you're in the right, even if you are.