Is this policy in place on Alaskan cruises? I don't recall from my cruise on Ovation this year. My kids are old enough that it didn't matter, but I don't recall seeing any young ones in the Solarium.
I expect it would be as safe as any public WiFi. If you are really worried, just use a VPN service. I typically do that on any public connections I use.
I always have to sign in on the website too. This happens on multiple browsers on Windows and MacOS. I use a password managers, so it's just a minor inconvenience.
The app seems fine though, that usually stays logged in.
My wife and I will be there. I've never been on Independence, so looking forward to a new experience. This is only my second RC cruise. The first was Ovation to Alaska in May of this year.