There have been quite a few non-mutant members over the years and I believe Hulk could potentially be one of them. I feel out of a lot of the teams in Marvel (outside of the Defenders obviously), the X-Men are the best equipped to handle having him on their roster depending on the version of Hulk.
The Hulk and the X-Men can relate to one another, with the whole being hated for existing, hunted and hounded, have their lives taken and or weaponized. I feel like Savage Hulk could feel a bit if comradery with them.
I also believe that the X-Men are best equipped to handle, restrain, and help both Hulk and Banner. They have a METRIC ton of telepaths that can help both Hulk and Banner in various situations. They can sense when he's being messed with, they can put Hulk in mental simulations to either calm him down or provide "aggression therapy", they can put Banner in mental simulation to deal with his trauma, and they try to suppress Banner's Hulk side if need be or vice versa. I also believe Banner and Professor Hulk would get along quite well with Beast and Forge, I also think Professor could develop a bash brother relationship with Logan. The only Hulks I could see not meshing well are Joe, Devil, Green Scar, and Fractured Son.
The X-Men have the capability to handle Joe Fixit and Professor Hulk. The only Hulks they couldn't handle are Savage, Devil, Green Scar, and Fractured Son. They could trick a childlike Savage, but not an intelligent Savage.
I dunno this was something I kinda thought about that could make for an interesting comic run. What do you guys think?