On instagram, it is a broadcasting and publishing platform and it is very clear that by posting a photo, on a non-private-account the photo can be seen and generally browsed by others.
A researcher who conducts a study of "looking at" 400k public instagram photos is doing a different thing than spoofing their location and auto-swiping through 400k lonely hearts.
Obviously people disagree with this since I'm getting downvotes for my position. This is certainly my opinion But I do feel like running a study against one isn't unethical while the other is.
Of course, that should be caveated that "republishing" the scraped data is unreasonable in both cases (IMO). I also think things like this artist http://fortune.com/2015/05/26/instagram-copyright-art/ are reprehensible... but that's art, not science and doesn't actually have the same expectation to abide by ethical principles.
The keyword is published for "browsing" and other things which are codified. You can't use it for mining data without consent.
There's a difference between public and public domain. Just because something is public, doesn't mean you are free to use it as you wish. You may still require permission to use it for tasks beyond the originally intended purpose.