Being owned and unsafe feels like the most natural fit. If multiple threads (or the interrupt handler) manipulate a register while you're already working on it could leave you in a very undefined state you have no idea about. In this case, rust makes you promise that you checked that this will be entirely safe.
You could also write wrappers, for example one that automatically turns off interrupt when you do a write operation or gives you a guard that lets you write and read the register, which turns off interrupts until the guard is dropped. Or one that has a lock or uses atomics. Plenty of options you can use here.
