If what Smythe says about drivers licences not being acceptable ID in several states is true, doesn't that make life difficult for those without passports, which I think is quite common with US domestic pax.
The proportion of non binary passengers can't be very high. Treating them all as male (for weight purposes only) shouldn't have any great effect on load sheets (unless you have a group going to a LGBT convention).
Double barrel makes a good point. I believe that the 1973 tube stock which serves Heathrow was designed to weigh its passenger load which was then used to adjust the breaking. Load weighing is used to determine passenger load in calculating railway overcrowding. You obviously need to calibrate the system properly that that shouldn't be a problem with modern technology. Obviously if you have miscalculated the weight of pax & cargo you may have to unload something before taking off and that could create headaches. I don't know what a system would weigh or cost but it could have avoided a number of incident reports that we have seen recently.