A strong culture of free speech is the clear solution to the problem you're describing. I.e. when both political factions censor, the only solution is a strong preference for free speech regardless of who is in power.
if the No Kings people truly want to be taken seriously, the best thing they can do is just admit they are wrong about their whole schtick. unfortunately the chances of that happening are exactly zero % since pride stands in the way.
watch and observe. literally nobody believes in free speech. people believe in policies and agendas, and "freedom" is just a tool used to push it. the right wing does this, especially in economics, all the time, where they want the rich to be "free" to fuck the poor. take a step back, observe the trends, and be honest with yourself, and it will be quite obvious that freedom itself is just a tool used in politics, nobody actually believes in it as an end to aspire to. this isn't 1980 anymore. milton friedman is long gone.