We were 18 minutes late to Mama Melrose's on our last trip and were turned away - they told me the grace period was 15 minutes (and were pretty nasty about it, frankly). I don't know if 15 minutes is the norm, because we are generally on time or early for our ADRs, so have never experienced this. This time, we were late because it took significantly longer than I thought it would to get through TSMM with FP+ and then walk all the way across the park with a toddler, a kindergartner, and grandparents in tow. My fault - I get that, but I was pretty annoyed. It would be one thing for Disney to turn away late comers if they consistently seated their ADRs within a reasonable amount of time. However, I can't count the number of times that we have waited 30 - 45 minutes past our ADR time to be seated at a Disney restaurant, without so much as an apology.
"Real world" restaurants seem to be able to handle reservations so that customers are seated very close to their reservation time. With all of the data that Disney has on guest habits, they should be able to handle ADRs so that their restaurants generally run on schedule, but this is apparently not a priority. Fine, but why should I be penalized for not accurately predicting ride and walk time, when Disney doesn't bother to accurately predict table turnover?