When in Instagram, CLICK on the BOTTOM RIGHT icon to get to your PROFILE page:
Image: Instagram. Courtesy iJustine.
Then CLICK the TOP 'GEAR' button to get into SETTINGS.
Image: Instagram Settings
SCROLL DOWN to PREFERENCES.
SET Auto-Play Videos to OFF.
Image: Instagram Preferences
You can now view Instagram photos and videos in silence.
Just like in the good old days of last week.