Open WhatsApp
Go to Settings
Tap Chats
Turn off Save to Photos on iPhone
On Android, open Settings
Tap Chats
Turn off Media visibility
To stop saving photos from a specific chat, open the chat
Tap the contact or group name
Tap Media visibility or Save to Photos
Set it to No or Off
To stop auto-download, go to Settings
Tap Storage and data
Under Media auto-download, set Photos to Never
Repeat for Wi-Fi and cellular if needed