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I looked at the profiles of a few people who I'm not friends with. I could view their profile photo in all cases (i.e. I could click on it and see the "large version" of it). On some of them, I could "like" the photo. On others, I couldn't—the link to "like" just wasn't there.
What setting controls this?
People you are not friends with can only like and/or comment on your public posts if you allow people to follow you on Facebook. If you disable this option, anyone who is not friends with you will only be able to see the "share" option and not be able to like or comment on your public photos.
