So I was dumb and started doing the institute quests before I joined the railroad. I'm only in the institute cuz the brotherhood told me to infiltrate it. I then went to the railroad and now they tell me to leave because I am in the institute. I was wondering if there was a way to join the railroad after this. I really only want in for the deliverer and ballistic weave. Since they aren't hostile I'm thinking I could get back on their good side. If I finish with the Minutemen, destroy the institute, and evacuate the synths would they be friendly again. Any help is appreciated.

Unless you use a save before you enter the Institute, no, you cannot join the Railroad now.

Sorry, you can no longer join them. You can only get it with a console command at this point if you're on PC, I wish there's a way to do it within the story frame to get Ballistic Weave without joining the Railroad.