If this was really the case then the onus would be leftists to articulate in simpler language. You can’t mobilize the common folk if you can speak the common language.
But most of the time its either the liberals lack the prerequisite historical knowledge or they just have antiegalitarian values.
I suspect the red=left association has to do with socialism which is haram in the US. Also the democrats go all the way back to Jefferson and were the conservative party until FDR.