You have zero privacy crossing national borders and if you aren't a citizen (or at least a legal permanent resident), zero right of entry.
In the case you are talking about, an individual thought it was a good idea to express support for someone that the US considers a terrorist and an organization that the us government considers a hostile foreign power. When the US government became aware of this, they refused her entry to the US.
Bluntly, if you are in any nation on a temporary basis (and generally if you aren't a citizen of that nation) then you basically have zero rights. At an absolute minimum the government can put you on a plane and send you back to whatever nation you are a citizen of basically on whim.
If you aren't willing to provide full access to everything on any electronic device you are taking across a border, then don't assume that you will be allowed to cross that border.
Encrypted cloud backups are your friend. And personally, I won't cross a border with anything but a mainstream, vanilla, device that has been factory reset before the crossing and will be factory reset after the crossing.
If you need a secure phone in a specific country on a regular basis, buy a Pixel in another country (ideally the US directly from Google paid for via shell company and shipped to a short term shady rental), bring it across the border in a vanilla state, load GOS onto it in the country in question, and store it in a safe deposit box in said country when you leave. Using a unique, strong, password of course. Transfer any data you need to/from the phone via secure, encrypted, connection to your own server.
If hostile nation states (especially the US) are part of your threat model then mitigating the threat(s) is going to be expensive, complicated, and inconvenient. Especially when you are under the physical jurisdiction and control of the US government. A "dummy profile" wouldn't really help.