Sounds like he's afraid you're going to break everything.

I'm sort of like him, but I'm concerned about germs. Like, I don't want anyone to touch my sh** because they have all sorts of germs. You can only touch my stuff if you use MY hand sanitizer, and I have to be the one to squirt it into your hands (cos I don't want my bottle getting germy). Or, you can wash your hands really well.

I wash my hands or use hand sanitizer all the time.

It started because I almost died 4 years ago from pneumonia... I wasn't feeling well, and then I called my doctor's nurse, who advised me to take DayQuil (cos she didn't know I had pneumonia, and neither did I). Well, turns out I'm deathly allergic to DayQuil. It completely shut my throat and my eyes swelled shut. I was all by myself and I couldn't breathe, but i managed to call 911 before I passed out.

I'm currently working on this problem in therapy. I don't know if I'll be able to fully get over it, but I know it helps me when people are patient with me.

As much as I don't like it, it's good when people slowly push me. Like, if they take baby steps, it helps. I think you should take this approach with your bf.

Before, I wouldn't let ANYONE touch my stuff, regardless if they washed their hands or not, but now I let them touch my stuff if they wash their hands well.

IMO, work with your boyfriend and see if he lets you touch his belongings under his supervision. Take baby steps. For example, take the tv remote and put it down on the table, then let him inspect it to make sure it's fine. Do this enough times (over the course of a few weeks) until he starts to gain your trust. When he supervises it, it lets him feel in control.

Tell him you promise you won't damage his things, and that he needs to trust and work with you if he wants to fix this problem. However, it's important that he sees this as a problem that he needs to fix. If he doesn't see it as a problem or if he doesn't think he needs help, then it won't get fixed.