No. Your database is one giant shared mutable state.
How is using a database safe then? Transactions."
Transactions are less an occasion where shared mutable state is made 'safe' during concurrency and more a situation where concurrent processes are forced to temporarily interact and operate in a sequential, non-concurrent, manner. They use locks under the covers. Databases manage to be parallel because different processes operate on different sets of data at the same time; they lock when two or more processes attempt to access the same row on a table. Transactional state access is still vulnerable to deadlocks and other difficulties of concurrent programming. This means that transactional state is not 'safe' in the same way that immutable and non-shared state are safe. It's just a much easier way of managing the kind of difficulties you have with shared mutable state than say, raw locks.