Popper apparently did not envision how social media would allow extremely powerful and rapid coalitions of opinion to be formed and to exert immense pressure on corporate interests responsible for allowing speech.
That is to say--it's complicated now. We need to reason from the principles, not from the precise phrases, because reality has changed since Popper's time.
If a hundred thousand angry twitterers have the same functional power as a government agency or court does to shape the actions of companies, and the companies are the only venue through which one can discover the viewpoint, then there is no functional difference between suppression by a government and suppression by vocal expression of an opinion.
I won't pretend there are easy answers. But I do think we're fooling ourselves if we believe outrage has fundamentally different reach than politically backed suppression.
As a practical matter, I agree with your advice: if you don't like what Joe Rogan says, don't listen to him.