This is not so much the case in rust because you only increment the reference count when you're passing around copied refs to an item. If you instead borrow a ref counted item, you don't need to increase the ref count - because rust will statically enforce that the borrow lasts less time than the item it borrows from (which is enough to keep the item alive). With good coding practices, you can eliminate the large majority of ref count increments/decrements.
Such cache line will (because it is adjancent to the refcounted data) almost always be in cache anyway. Rust's refcounting is much cheaper than C++'s refcounting because it doesn't need to be atomic. (There is a separate type for atomic RC, and it is enforced by the compiler that you use it when needed.)
Modern generational GCs are reasonably nice on caches in most cases.