First, Ina Fried in her initial challenge to Harris used the phrase "speaking their truth about their identity". But this language either denies objective truth (if there is objective truth, "my truth" and "their truth" makes no sense at all) or, at best, it is highlighting that the matter is so personal that it cannot be objectively understood or challenged which is exactly the opposite of what you want to argue when saying that people should make allowances for trans people.
Second, Franklin Leonard in his otherwise cogent question about the dangers of speaking truth to power, says, "...when challenging orthodoxies historically, to speak their truth". Again, this is a fundamental misrepresentation of what is going on: when you speak "truth to power" as opposed to "opinion to power", your premise is that there is an objective truth. That is what gives the phrase its weight: power has it wrong but because it is powerful cannot be easily corrected.
Even if neither person actually intended to advocate for a truth-denying postmodernist perspective, this is, in its own tiny way, stepping along the path towards the death of rationality, as Harris charges.
This isn't to say that the right does better. Indeed not! It's just that the left and right are marching arm-in-arm, with "my truth" and "alternative facts", away from reason.