Every side always believes their cause is just. You think Republicans vote that way because they're innately evil? No, they vote that way as they genuinely believe that's what's best for society.
Are they wrong? In my view, yes. If I were an American, I'd be a Democrat all day long.
But what they believe is that what you call making things better would ultimately end up in societal destruction. The way you convert that mindset (and incidentally bring the Republican party away from extremes and more centre right) is by gradually making a success of it. One step at a time. No government is perfect, and for that reason when you get a radical government who goes for ideological broke, then when things go wrong the ideology itself is blamed.
It's why I said there's never a "good" riot, because no matter the cause that underpins it, its still a bloody riot and it therefore tarnishes that support. Hence why you see Extinction Rebellion people pulled off trains and battered for wanting to save the planet; because constant, annoying protests tarnish and overshadow the whole message.
Politics - good politics - is all about nuance. Fighting some battles, leaving others, understanding that the overarching aim is to win an ideological war. This view has been completely and totally lost in the last few years as everyone pitches their tent on one "side" and wants to destroy the other.