There isn't a doubt in my mind that NTs struggle with this too. What I think the difference is: it's just not an everyday challenge or concern for them. I think the difference is that NTs can walk into a room full of strangers and naturally just pick up the social cues/rules while knowing instinctively how to not break any of those rules until they are understood. I do know though, that several of my friends who most certainly are not autistic, have embarrassed themselves by breaking social rules on occasion.
The other difference I think is that (this is based on personal observation alone) is that confidence and "attractiveness" allows someone a great deal of flexibility in breaking social rules without creating awkward moments. I think that's the other thing NTs do, is they fallow a set of unwritten rules, but at the same time create their own and know how to send non-verbal cues alerting people of their unwritten rules.
And finally, I think when NTs do make social mistakes, which they certainly do, they can see the social mistake more clearly than those of us on the spectrum. Because I think they can see the situation in it's entirety more easily, their social mistake then doesn't cause them much embarrassment. Also NTs almost certainly know how to recover quickly and seamlessly from a social screw up than those on the spectrum.