It's private for a reason and you should respect that. You have to add them as a friend, otherwise if there were anyway for Mac it would be creepy. I'm not sure if there's a setting to have it always private or not even if friended so I think you're out of luck.
Bad news for you, no matter what device you're using, none of those "Facebook private profile viewers" actually work, Not only do they not work, but they're also a really bad idea.
Why?
Here's a few reasons you'd want to forget about private facebook profile or photo viewers for Mac, PC, or even Android, WIndows Phone, or iOS.
In light of all that, I'd say it's probably easier to just man up and send the friend request.
Or if you don't get one accepted, leave it at that and move on!
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