Alright, so here's the thing. I got the quest for Rex to be my companion. The first step is to speak to Julie Farkas. You see my problem is that I accidentally misclicked something and stole from the Followers of the Apocalypse a while back, and now whenever I enter the camp, I get shot to pieces. Any tips to get around this, or is this quest basically ruined for me now?

No it's not ruined, or at least I don't think. If you know the location of Jacobstown then go there and talk to the doctor inside the lodge. This SHOULD work because that's where it all ends up to, with the lady doc telling you to go there and whatnot. But it might not work because you haven't triggered anything because you haven't talked to Julie. But still, try going to Jacobstown; it's a hell of a walk from Vegas. Take the highway that goes north, then you'll see a road leading into the mountains on your left.

umm maybe reload the game?

if the doctor in jacobstown doesnt work and you dont have an earlier save i would recommend trying to get the followers to be friendly to you again. you just have to find someone from the faction not in that area and do a quest for them or something else.....i may be wrong but if you do the helios one quest the one of the scientists you talk to is a follower and if you complete the quest (cant remember the specific name) you gain fame for the apockalypze (dont know how to spell) followers...again i might be wrong but that is what i seem to remember about them