I have been traveling diapered for years. Destinations across North America, Europe and Asia. I use the same preparation as others on this thread: bring extra diapers in my carry-on in case my checked luggage doesn't arrive with me. I have never had any issues. Of course, there were the rare moments when a security or customs person opened my luggage and saw my diapers, or the security scanner detected my ointments or powers. But those situations didn't yield more than an inconvenience and potential embarrassment. Only rarely have I been stopped because a body scanner detected my wet diaper (or urine bag when I have a catheter in), but these situations were always quickly cleared up when I told them exactly what it is they see or notice. I no longer care to be dry when going through security. I have never encountered an unprofessional reaction from either security, customs, or airline staff. They have not always been kind or courteous, but never unprofessional as long as I stood my ground and, through my demeanor, demanded to be accommodated for my needs.
One piece of advice: to prepare for very long flights (over 8 hours), I use a lot of diaper or barrier creme in anticipation of sitting in a wet diaper for potentially long periods (take-off, turbulences, meal service). Plus, loose-fitting clothes are always a plus. Onesies under comfy jogging pants are ideal: they hold things in place and prevent the accidental showing of my diaper or PUL pants.
Safe travels!