Instagram keeps adding new features and the latest is particularly troubling, privacy-wise.
The Instagram Direct messaging component now shows if you're currently active on the app, or when you were last active - consider it the equivalent of WhatsApp's 'last seen'.
The good news? You can turn it off. In Settings, use the toggle to turn off the "Show Activity Status".
Still, it should really be an opt-in feature instead of being enabled by default. It makes stalking easier, which could lead to bigger privacy problems.
Nice job, Instagram. Not.