Most companies, even in the EU, say that workplace systems are for performance of job duties only. That doesn’t mean it’s necessarily legally enforceable, but either way it’s a much more nuanced argument than it’s being portrayed as.
If I have a right to use company systems to organize a strike, how do they then account for those messages in their normal record keeping and compliance procedures? Do they also have to retain them for x years along with everything else? If they have some kind of mandatory audit procedure how do they separate those emails out so that they aren’t reviewed on a regular basis? If someone sexually harasses someone in what is not specifically a workplace communication but do it over company email how does that impact their liability? How does it impact what materials may have to be handed over for any kind of other lawsuit?
If I were going to protest the company who is actually paying me presently I would never do it using their email system so for me it’s a moot point, but it’s not quite as cut and dry as an evil corporation trying to restrict the rights of workers.