My campus has both present, but there's a very clear distinction in treatment. The only really conservative organizations on campus are the religious groups, and the university has pretty effectively browbeaten them out of any activism with threats to force them off-campus. So they focus nearly exclusively on charitable works, private events for their members, and MAYBE handing out Gideon Bibles (or the Bhagavad-Gita in one case.)
Lefties, then, pretty much have the run of the place, but there's so much infighting that very little ever gets done. The Palestinian advocacy group has essentially become the Arab identity group and doesn't want to deal with anybody. The black student orgs cooperate amongst themselves but they're almost completely apolitical (preferring instead to focus on making connections in the corporate world to set up their members with internships, invite speakers, and whatnot; and to throw the occasional party) and deeply resent other groups for essentially feeling entitled to their support because they're black and therefore oppressed and therefore "allies." The LGBT groups are so crippled by infighting that the University has cut funding from them to let them work through all the splintering and rapidfire leadership changes, and their internal toxicity means other organizations are unwilling to work with them, rightly fearing they'll bring it along. It's similar stories with all the rest of them.
TBH it's super funny that the stereotypically intolerant right is able to organize and cooperate smoothly with organizations centered around different ideologies, denominations, or even religions; while the tolerant left is neatly segregated by their mutual animosity.