iOS 9.3 update breaks links in Safari, Messages and Mail apps

I was at the Apple Store in NYC At 1am yesterday. None of the people there knew how to solve it. I looked online and there are, by now, thousands of users in several threads in Apple forums complaining that links don't work. Here is some more info:

This isn't just affecting 9.3, it's true also on 9.2.1

Don't bother wiping and restoring your phone, the problem comes back. My guess is that it was triggered by something in the Apple WebView APIs that happened recently, because it started happening on my phone for no reason this Friday (with 9.2.1) and most of these forum messages are from the past few days.

Apple hasn't responded yet and 9.3 doesn't fix this problem.

For now, use Google Chrome. Long-tap on links in Safari and other Apple apps crashes the app. However, thankfully in Chrome for iOS, it works (even though it also uses Apple's WebView). You can follow links via long-tap and copy-pasting the link into the Address bar.

Finally, if you're wondering why some mobile links still seem to work - those are the ones enabled by javascript handling of tap events, that don't use the regular mechanism of loading a url.