The problem isn't the hate speech or the enforcement really.
The problem is that these powers have, can, and will be abused by petty bureaucrats, power-hungry law enforcement, the government itself and, as a result, enable actual tyranny.
Rather than disregarding the concern, how would you propose the overreach should be handled? And is it possible to handle the overreach before it harms citizens caught in the middle, or can it only be dealt with after innocent people are on the wrong end of the overreach?
And innocent people that get harmed by non action are irrelevant? Laws can and will always be abused but if they are about online discourse the only possibility seems to be that there will be nothing but abuse. As long as you are in a country with an intact democracy and separation of power you'll be fine and if not vote against it.
Civil servants desperately trying to hide their mistakes won't believe they are overreaching, and neither will their friends or the politicians who would held responsible by the media.