Did progressives handle the Lia Thomas incident well?

[100% pro-life no matter what]

I think what happened here is that the median American believes something along the lines of "transgender people aren't really the gender they identify as, but should generally be treated as they identify to a certain point".

This situation was one where people felt that the "certain point" had been reached.  There are two conflicting beliefs that many people have (that they aren't "really" that gender, but that they should generally be treated as it nonetheless).  In this specific context, the former seems to have won in the minds of many Americans.