Is there a setting for preventing Facebook from automatically publishing to my timeline whenever I change my profile picture? I tried hiding it from timeline after changing but it still shows up in the news feed and the privacy setting is also set to public so the whole world sees it. I tried deleting it from the timeline but then the new picture gets deleted so I get the default one.
Your profile photo is always public and there does not (currently) appear to be a way to change the default audience the message that gets posted to your timeline when you change it.
It looks like all you can do is, after the message is posted on your timeline, change the audience to whatever is most appropriate (e.g., "Only Me"). This is, of course, like closing the barn door after the horse has already bolted, because anyone who gets notifications of you activity via other means (e.g., email) will still see the message.