At first, I tried to think my own way through. (Ironically, a Google search in Safari pulled up a link to the blog that seems to hold the best diagnosis and workaround - one which users here found and linked to ( https://bencollier.net/2016/03/how-to-fix-ios-9-3s-broken-safari-links/ ), but I couldn't access that link via the iPhone 6S at that point. In later posts here a user quoted from the documentation for the canOpenURL: method of Swift and Objective C. Sounds promising to me (speaking as one who has been introduced to coding Android apps, but not Apple apps. The principles are basically the same, it seems.Methods and libraries.
But before that I personally had had some symptoms of cloud-related issues that are not obvious: I noticed awhile back that an app - Newsify - stopped working until I turned on iCloud after an iOS update. That was probably about iOS 9.2 somewhere.
Meantime, my iCloud ID had/has kept my old email address.
I wanted to ditch references to that email address (I have a new one), and had changed my Apple ID online, figuring that doing that would cause the new ID to propagate where necessary. Apple, when I got this first iPhone (actually my first iDevice). That somehow didn't happen or the procedure wasn't clear, or something wasn't thought out.
Early in my experience with iOS, as I recall - and that started with an iPhone 4, actually (I skipped iPhone 5), the Setup Process said that the email address that drove the Apple ID would not change - and to be aware of that. That seemed odd - whenever people move (geographically) they tend to look for the best local ISP deal. Sometimes job changes change the email.
I am aware that some people avoid this email churn effect by using a less geographically variable email, like Gmail. I am not in the driver's seat for ISP choice since the recession: my spouse's choice of local ISP "rules."
Apple subsequently seems to have realized that the email address sometimes has to change for good reason, and made that possible.
Apple didn't warn me to sign out of iCloud when I eventually did change my Apple ID online, and it seems that I therefore wound up with an iCloud ID that didn't match my new Apple ID.
Despite that ID clash, I did minimally enable iCloud, and therafter Newsify worked (prior to iOS 9.3). So I know at least that the Newsify app passes its stuff through Apple's cloud, or is somehow leveraging cloud-related technical capability...
Apple has posted a support note about a mismatched iCloud and Apple ID and iOS 9.3. So I am probably not alone.
<Link Edited by Host>