I'm kinda in agreement with you. The right has a seemingly limitless supply of ammo, but I don't see that as a case for not caring if someone gives them more.
All it takes are bad slogans to entrench their beliefs. "All cops are bastards", "math is racist", "defund the police", and "all white people are racist" make them think the left are insane.
More than anything, this is a war of optics, the left are more educated, more tolerant, more generous, and if we are going to deconvert anyone from the right, we need to show them we aren't morons.
Reflexively jumping to Godwin's law is the fastest way to lose.