What has worked for us is a not ever hiding anything from the other person but not searching there stuff unless there was a reason eg. Me going through his email to find a email that one of us needs. Him going through my phone to find a document. Etc... We don't need a special permission to do it but we all always tell the other person hey I need this from your xyz. Or hey I needed this do I went through your xyz. This is a very rare thing but has happened a few times in our 23 years together. I would never just search his stuff to see what's there.
Respect and trust are massive thing in a relationship without them it will eventually break.