Snapshot_isolation_state_desc on a Read only/Stand by Database
SQL Server always seems to set snapshot isolation (SI) on when a database is made read only. I have no idea why it does this, but it does.

You can try to turn it off, and the ALTER DATABASE statement will succeed, but snapshot isolation remains enabled while the database is read only.

One theory is that setting SI prevents unexpected errors for people running an SI transaction and accessing the read-only database, but it seems like there should be a deeper technical reason.

In any case, the behaviour is "normal", so you should not worry about it.