Well if they project then they never have to look at themselves.
I'm thinking many Repubs project because they don't want to look at themselves and what they've devolved into and if they did, they'd have to face reality square in the face and admit to some very despicable things they've done/are doing to defeat democracy and have been in denial about it for decades.
Much easier to play the victim card and blame everyone else for the pathetic circumstances they've brought upon themselves. They need the votes from their racists, their incels, their fascists, their militants and their religious fanatics to win gerrymandered elections. That's how bad things are for them. Projecting is a knee jerk defensive reflex the Repubs have had to increasingly rely on the more they find that they're isolating themselves out of the mainstream and into the realm of the fringe.