Above all, liberals believe that getting to the objective truth is the fundamentally necessary condition that must be achieved before we can build a good order.
I can't agree. Liberals are not looking for the objective truth about racial or sexual difference. Anyone who looks for it is accused of bad motives, and anyone who purports to find it is accused of bad science. All by liberals.
I have no problem with avoiding unsettling truths. The American origin story is a myth, as it should be. So are politically necessary notions of demographic equality. I am not saying we should censor speech that questions these myths. I am saying that the search for objective truth about them is not a reason to support free speech. The "search for truth" argument only applies to issues in the Overton Window. That window should be wide, but not unlimited.
The political basis for free speech is not the search for truth but the exchange of information about our fellow voters. We need to hear what people think so that we can act and vote accordingly. Even the most vile opinions need to be stated, because we need to know that they are held. But this is strictly a political standard for the political arena. Academic freedom and other forms of "free speech" can be more limited.
Free speech makes it less likely that really awful people will seek high office, win high office, or retain high office. No place with a free press is run by tyrants. Fools and knaves, yes, but not tyrants.