For what it's worth, I just read this thread on Easter Sunday, and when I switched my search engine in Safari to Bing, the one link I then tried did work correctly. Before I did that, I opened my google email and tried clicking on one link in one message in my inbox, and that also worked correctly.
I know this doesn't help those of you who it doesn't help, but it's one more voice in the wilderness with one more piece of experience.
The irony of trying and not being able to use one's iphone to try to find solutions to a problem the iphone is having has not escaped me! 😠
Now then---10 minutes later, here's another data point, and this one is much curiouser than the first!
I just stood beside my wife, who has exactly the same phone as I do. She verified that she installed ios 9.3 sometime between 48 and 72 hours ago, in the past few days. For me, I did it 24 hours ago, on Saturday morning. She verified she's using Google in Safari. She typed in a search phrase and Google displayed the usual list of links. She then clicked on one of them and it worked perfectly! I hate her!
We verified her Safari settings and mine are identical. We checked both phones for software updates and both phones reported our ios 9.3 is up to date.
So I then went to my Safari, entered the exact same search phrase, got the same set of links in Google, tapped on exactly the same one she had tapped on that worked for her, and guess what! Nothing. Nada. Zilch. Zip. No action whatsoever by my phone! 😮
Go figure.