Q: Is it mechanically safe to coast in neutral?

Technically, least cost operation is attained if engine idling (at stops) does not exceed 60 seconds and, indeed, some studies put the threshold as low as 10 seconds. Certainly 60 seconds is a conservative estimate. This is why "start-stop" features on modern engines have become popular; "start-stop" saves money. As a practical, and most importantly safety matter though, unless your vehicle came equipped from the factory with start-stop technology, do NOT turn your vehicle off at intersections because that practice will substantially increase the risk of a collision and has the potential to impede traffic flow as you attempt to mimic the operation of what is ordinarily seamless start-stop technology. In all other settings, though, as noted if your vehicle is sitting idle for as little as 10 seconds you will save money turning the vehicle engine off. As far as shifting from drive to neutral and back again, although there is no damaging effect in an automatic transmission, such a practice is NOT recommended, again due to the safety hazard such a practice creates. During these periods when the transmission is in neutral, you have no ability to accelerate the car, if it becomes necessary to avoid a collision. You also loose all engine braking, there is no appreciable gas savings, and the manual shifting becomes a driver distraction. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.