I assume they'd have to work extremely hard to compartmentalize some things.
I want to know if it's regular practice to post political officers and covert intelligence officers to Belle crews to ensure such things aren't getting "accessed" by various parties.
Baseless speculation you don't need to include if you use this for an update:
For example, I'm a Yank and will probably play one for my first play through in game. Let's say by hook or by crook my Jarhead ass enlisted in the 1930s and I ended up in one of the various Pacific postings for Marines. A fair few of those had regular visits or chances to run across Japanese warships and would have certainly been on the list of places about to be raided by Morgana 1 September, 1939. Albeit at mid afternoon or late evening since everything kicked off with the Schleswig-Holstein firing the opening bombardment of the war... by the European perspective. So it's perfectly reasonable for a Belle to pluck my sorry ass out of the water after getting blown out of a defensive position or my previous ride being sunk at her moorings with a "Get in Gaijin we have a war to win." on day one.
We've covered that previously. That's gonna be a *huge* clusterfuck for the Japanese government once they begin unfucking things. Japan *still* isn't terribly friendly to non Japanese but in the 1930s and 40s it was *really* not exactly welcoming. Seeing an American officer on the bridge of a Japanese warship as anything but a prisoner probably would have been terribly upsetting for certain individuals in the Japanese government. Would they deal? Depends on how much they want to keep the kami happy... and if they think they can get away with eliminating someone quietly without pissing her off.
For these nations I assume they'd deal partially by ensuring a captain of their nation remained as executive or first officer. Establishing a second radio room with one dedicated to INPF communications and another reserved *solely* for IJN communications (or whatever nation) with tight security would also let parent nations keep a handle on their assets and keep them in the loop... without letting cryptography assets into what nearly amounts to public consumption. Some Belles you'd just have to cut out of the loop entirely. Nurnberg for example would probably be fine to have a second Kriegsmarine commo shack with an enigma machine and dedicated Kriegsmarine sailors manning and guarding that post. She is unlikely to violate security and share that information with a foreign captain. Another Belle might not be assessed as being so reliable.
Of course part of this is the idea about cutting Belles out of conventional forces with the INPF... but there's a lot of cracks in that as a solution.
"Hey we've got this great new ship that's a secret from the world. Look at this beauty of a battleship."
"Gorgeous, what's her name?"
"Yamato... is that a raid siren?"
"I see a lot of fog... most be those sea witches."
The two IJN officers watch as the Yamato comes to life on her own volition and snaps her mooring lines, maneuvering to unmask her 46cm guns and engage.
Now the largest battleship made by human artifice, the pride of the IJN... is out of the war and serving with the INPF. That's a big example of a common problem. Various advanced Japanese destroyer types, even the Fubuki class special type destroyers that revolutionized the concept of destroyers in the 30s could provide all manner of useful information to the right parties. That's discounting some of the special weapons systems like oxygen torpedoes. Hell a guy being able to observe the ship's performance in combat from her deck, taking notes and sending it back to ONI (US) could have a massive impact on conventional engagements. "These Type 96 AA guns are fucking awful. Their deficiencies are thus..."