There is always state somewhere, the question is where it should be.

Global state is the input to the program, and a new global state is the output. Given identical inputs, it will always produce the same output.

This is the entire principle behind ACID, and mutation of global state is a common approach for functional programmers regardless of whether they they are using a DB or not.

If a DB were not fully transactional, or if your queries of the DB are not deterministic themselves, then we’ve moved out of functional territory.