I've flown with diapers several times and never had that experience. I used to put my diaper in my laptop bag and then put it on after I cleared security so that it wouldn't be visible in the body scanner, but after close to 4 years 24/7, I don't own any underwear anymore and I don't like going more than 30 minutes or so without a diaper on, as it gets uncomfortable. So, I swallowed hard, and wore a diaper through the body scanner a couple of times now. The first time, the lady who was operating it asked me to pull up my pants and go through it again, then asked an older guy who was supervising to look at the screen, and he told me to go through the metal detector instead, which of course I passed. The second time, in the UK, the operator didn't even blink, just said "You're good". The rest of the times, I got lucky and ended up being directed to a metal detector instead of a scanner.
On all of those occasions, I also had a diaper in my carry-on or laptop bag, and they've never been mentioned or inspected. I'd imagine they see them all the time. But I have mentally prepared myself for the time when I get asked over to secondary to confirm I don't have drugs or explosives tucked around myself, and I'll have to clear my throat and say "Uh, it's a diaper...", and hope that they take my word for it!