Instagram recently announced support for photo uploads via its mobile website. But the desktop version of the site still doesn't offer a way to upload images from a Mac.
I tried changing the user agent in Safari to "Safari — iOS 10 — iPad" and doing so does in fact enable photo uploads from the desktop. And the interface looks nice too!
To enable the ability to change Safari's user agent you'll need to go to the Advanced Preferences pane and check "Show Develop menu in menu bar."