Conservatives want to conserve the status quo. Progressives want to see society progress. Liberals want liberty. Authoritarians want strong authority. "Social justice ideologists" doesn't roll off the tongue, but it does a decent job of conveying who we are talking about.
Social injustice ideology?
No, they want to see it change. Not all change is progress.
Which is what I said
Nope, that is not what conservatives and progressives want. Conservatives want to keep that which is proven to work and only want to change things which are proven not to while progressives want to change that which has been done for a long time because not doing so leads to stagnation. Society works best when there is a balance between conservative and progressive attitudes. When things work well they are better left alone - this is where conservatism gets it right - but when the situation changes those things which used to work may need to be replaced with something else, traditions be damned. That does not mean all traditions need to be kicked to the curb - they often form the glue which holds society together - which is why a balance between conservative and progressive attitudes works best.
"The scourge of social justice must be stopped!"
From a grim tactical point of view, it is smart to start finding ways to force an antagonism between your evil teens and regular liberals. I think that will work very well in the long run.
Because gosh darnit we must keep those statues standing up! Literally can't think of anything more important.