Ha ha yes, you're normal!!! Well, normal in that lots of people are like you.
I have had this convo before and there does seem to be a split between public shiters and non.
I am in the non group with you. I would only ever shite in a public loo if my need to go was such that it was going to wreck my day. Luckily i am very regular and always go on first waking. So i never need once i have left my house or hotel room.
I am fine going in a hotel en suite room. The situation where i would never go is in public loos where there is a queue.
Last night, for eg, i am at the theatre during the interval. Huge queue at the ladies and only 4 toilets.
Someone goes in one of the loos and is clearly having very smelly diarrhoea! I mean, cannot be helped but if i had needed diarrhoea in that situation, i would have gone during the performance when the loos would have been empty.
It is just a personal thing. And if the flush fails, you just do not want someone seeing your shite!
OP - take some immodium before your flight. Save your fears!!! It will stop your bowel for 24hrs.