Apple published iOS 9.3.1, which should fix all of the issues.

There have been numerous threads and articles about the iOS link bug, with many of them posting false information. This bug is not limited to iOS 9.3 nor does it have much to do with the update itself. It appears to be caused by the Shared Web Content Daemon, which goes into a crash loop after the Booking.com app tried to register too many universal links. Perhaps other apps are to blame too. I won’t bore you with all the details and get to the point: the method I wrote up below fixed the issue on my iPhone 6S Plus.

If you miss or modify a step, it might not work!

Recipe

1. Connect your iPhone or iPad to your PC or Mac via Lightning or 30-pin cable (not Wi-Fi) . If necessary, accept the ‘Trust this Computer’ message on your device.
2. Launch iTunes (if not already launched).
3. Turn on Airplane mode.
4. Uninstall the Booking.com app if you still have it installed. If not, then go to the next step — this should not be an issue.
5. On your iPhone or iPad, go to Settings → Safari.
6. Set your Search Engine to Bing or DDG.
7. Disable the following:
   • Search Engine Suggestions.
   • Safari Suggestions.
   • Quick Website Search.
   • Block pop-ups.
   • Fraudulent Website Warning.
   • Advanced → Javascript.
8. Disable all enabled Content Blockers (eg. 1Blocker — this is my preferred one).
9. Leave your device connected via Lightning cable and in Airplane mode.
10. Turn your iPhone/iPad off by holding the Sleep/Wake button, then sliding the on-screen slider.
11. Turn it back on by holding the Sleep/Wake button. Keep Airplane mode on!
12. Go into iTunes and install the Booking.com app — select your device then go to the App tab and press install.
13. Press Sync, to actually install the app.
14. Keep Airplane mode on!
15. Run the Booking.com app. When asked if you want to accept notifications and/or GPS access, do not grant them access! (Just say no.)
16. Double-click the Home button to launch the multitasking screen and kill Booking.com by swiping up on it.
17. Uninstall the Booking.com app.
18. Turn off Airplane mode.
19. Turn on everything you disabled or changed in steps 6-8.
20. Smile (or read below if it didn’t work).

This worked perfectly for me. Let me know if it helped you too.

Many thanks to Rosyna for the original method.

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Update — 29/03/2016, 13:17

Clarified step 1 — you need to connect via cable, not Wi-Fi, to your Mac/PC.

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Update — 29/03/2016, 18:07

Ben Collier has posted an updated recipe — 2.0 if you will — which might help those of you who didn’t luck out on mine. Just follow this link to his site.

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Update — 31/03/2016, 19:00

iOS 9.3.1 is out — it should fix any issues which you might have.

iOS 9.3.1 Is Out — It Fixes the Safari / Mail / Messages Link Bug