I don't know you're experience with hash functions, so you may already know what I'm about to say.

This is a minor example, but since you asked...

https://github.com/Cyan4973/xxHash/blob/dev/xxhash.h#L6432

That's an example of a fair number of accumulators that are stored as XXHash goes through its input buffer.

Many modern hash functions store more state/accumulators than they used to. Previous generations of hash functions would often just have one or two accumulators and run through the data. Many modern hash functions might even store multiple wider SIMD variables for better mixing.

And if you're storing enough state that it doesn't fit in your registers, the CPU will put it into the data cache.