Hi, I have the same problem as you, guys.
From what I've found this seems not to be limited to Instagram only, but to all those pages that use the new CSS System Font stacks — please check System Font Stack Experiments
I'd like to share what I tried, just a clue, not a fix tho.
I logged on my mac as a new user and the issue wasn't present so I guessed it was not system-related.
So I started investigating my standard user folder and I was able to recreate a situation in which this doesn't happen but unfortunately this is not a permanent fix. 😟
I've discovered that deleting Apple Type Service preference file (I guess it's useful only if you use Font Book as a font manager):
~/Library/Preferences/com.apple.ATS.plist
"fixes" the problem.
Unfortunately the font manager I use — FontExplorer X Pro — needs "automatic font activation" in Font Book preferences be disabled to work properly, so FontExplorer RECREATES that file each time it can't find it...