Instagram- How to keep activity status turned OFF?

1. On your account profile, tap  at the top right (for android) to see settings option.
2. Tap Settings at the bottom of the page then go to > Privacy and then > Activity Status.
3. Tap the slide switch (if it's ON) next to Show Activity Status.

This will turn off your activity status.

Note: Instagram also notifies you, if you turned off you won't be able to see others activity status as well. Make changes according to your preferences and interests.