WhatsApp statuses
Turn off read receipts
Settings, Privacy, Read receipts, off. Your views on other people's statuses aren't shown, but you can't see your own status viewers either, and blue ticks are gone in your private chats too.
Privacy mode in MsgSaver
Open WhatsApp from MsgSaver's tray menu with Privacy mode on and watch the status there. The poster doesn't see you in their viewer list. Your WhatsApp settings don't change, so you still see who viewed your own statuses.
Instagram stories
"Anonymous story viewer" websites
These sites load stories from public accounts without logging in. They can't show stories from private accounts, they're full of ads, and some ask for your Instagram login, which you should never give them.
Airplane mode
Loading stories, going offline and then watching them used to work. Instagram usually sends the view when you go back online, so it's not reliable.
Privacy mode in MsgSaver
With Privacy mode on for Instagram, watching a story in MsgSaver's Instagram window doesn't add you to the viewer list. You're using your own account, so it works for anyone you can already see, including private accounts you follow and close friends stories you're on.
A word on fairness
People post stories expecting to see who watched. Privacy mode is for things like not wanting an ex or a boss to see you looked. It's not a way to follow someone who blocked you, and it can't: you only see what your own account can already see.