I have this issue as well, iPhone 12 Pro Max. I click tag, get the message to tap the screen to tag someone, but tapping the screen doesn't do anything. Nothing happens at all.
But it's not just Instagram. It happens on at least two more of my apps, in very specific circumstances. One is Duolingo, where the entire app works perfectly EXCEPT for stories, which are supposed to open when tapped, but 19 times out of 20 nothing happens when I tap them. Only occasionally does it work properly, seemingly at random. No one on Duolingo forums seems to have this problem. The other app is Headway, where I can't tap the books to open them like I should be able to.
It's not an internet speed issue, and all other apps seem to work just fine. This is my 2nd iPhone 12 because the first was buggy in a different way. What the heck is going on? So frustrating.