That's the real issue, however fundamentally I don't really see an issue if saying certain things publicly makes you effectively unemployable.
> In Europe there's a specific list of reasons which can result in work contract termination.
It varies by country but I'm not sure it applies to illegal/banned speech? Also in Europe you can be convicted and fined for quoting the Hadith while not being a Muslim* and the ECHR doesn't see a problem with that (which unfortunately proves that "freedom of speech" is just not a thing in Europe).
Germany is putting people in prison (for as long as 5 years) just for their speech (as false and repulsive as it might be. How is that better than making those people "unemployable"? Which probably wouldn't even be the case since there (unfortunately) are still plenty of people who'd hire nazi apologists (both in US and Europe).
*https://en.wikipedia.org/wiki/E.S._v._Austria_(2018)
> is such a fantastic deal and an example of freedom of speech.
IMHO it really depends on what opinions exactly did you express. Again I don't see how is it any fairer to impose your personal controversial views on your employer (even if indirectly).
This is the problem because 99% of people are effectively dependent on their employers, and there's huge power imbalance between employers and employees.
In Europe there's a specific list of reasons which can result in work contract termination. This means that the employer cannot fire me just because I posted on Facebook "vote for party X for better future". This means that I feel free to post this because I know nobody will ruin my life over that.
In most US states there's a specific list of reasons why people cannot be fired - which means they can be fired for all other reasons, and "posting on Facebook that you support given party" does not belong to that list, which means that you can be fired for that, which effectively makes you think twice before you say things publicly.
I really don't think that "you don't go to jail but you have your life ruined by being fired and becoming unemployable" is such a fantastic deal and an example of freedom of speech.