You can criticize a mayor or anyone else in the EU, but you have to show a minimum level of decency while doing so. I understand that's not a very popular opinion in the country that elected Donald Trump president.
Something to think about:
Imagine a mayor makes a decision with which a small, but very vocal minority of the town's residents strongly disagrees. Some of those people hurl personal insults at the mayor on a regular basis. After some time, the mayor can't put up with the constant abuse any more and resigns from office.