if for example a bank wanted to build a site on the network.
Is it possible to have the site on Safe and on Clearnet?
If a user logins in to the site on Safe, then say logs in to their account and makes a fiat money transfer, this would be recorded on a database. But then how would the clearnet version know of this and sync?
The clearnet data store on the backend would be built talking directly to the safe network. If you access via clearnet all it would have to serve the data back from the safe network through a centralised server and to the customer like a proxy. Assuming the implementation secured your data then going via clearnet would require trust in the bank to handle requesting and delivering your data via your access means.