It offers no protection in a case like this between two non-government entities.
In Europe the government does that though, so "even in the US" is a nonsense argument here, the US is horrible at protecting individuals rights against oppressive companies.
I am not certain about such laws that could apply to this case, but there are already plenty of laws around what you are allowed to retaliate for etc. Just like USA makes it illegal to fire based on race or to fire union organizers, it is the same principle.
https://en.wikipedia.org/wiki/Charter_of_Fundamental_Rights_...
Then the "freedom of speech" argument is even more irrelevant, in my mind.
So just because US freedom of speech is limited to government doesn't mean that applies everywhere.
USAs free speech laws mostly just bans governments from retaliating, but a more encompassing law would also ban corporations from doing so as well, there is no reason you should fear speaking up just because the corporation might retaliate and ruin your life. USA already has such anti retaliation laws for companies in some cases so there is nothing unreasonable about it.