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I don't know what kind of smartphone you are using but every photo someone texts me ends up in my Android gallery.

I didn't know Android did that. If you're texting tons of photos I can see it getting out of control

iOS doesn't save images people send you automatically. It will save pictures you send to others on your Camera Roll though.

WhatsApp on iOS does that. Every Picture I receive is automatically saved.

You can simply turn this off in the settings ("Save Incoming Media": OFF).