Other users never see your dashboard unless you share it with them (Settings → Sharing); the database itself enforces this.
The person who runs Money can technically reach all data: it lives in a database they administer, the daily price and snapshot jobs read every account, and admin backups include everyone's rows.
Stock tickers are sent to Finnhub and property addresses to RentCast to look up prices. No bank logins are stored — everything here is entered by you, so leave out account numbers and passwords.