Calling it "the other side" is a false dichotomy. There's certainly advocacy groups like Sea Shepherd but they don't wear cloaks of subterfuge to try to distance themselves from their structure and purpose like say, the heartland institute which among other things, was, at the time secretly, funded by Philip Morris to deny that smoking had health impacts.
That's a different class of spin. But sure, the Brookings institution is mostly neoliberal radical centrist, fine.
Well then I guess the other side operates on social media/etc and pushes ideas like we should give up our public spaces to homeless encampments and police aren't necessary. Or things like rent control, all of which do not work, ever. I don't think the reason "leftist" policies fail to gain traction is because of think tanks; the ideas are just bad and reek of armchair socialism/virtue signaling.