Hi there Cinderella ... I travel quite a bit internationally and domestically with my ileostomy. So I do not have the luxury of irrigating or having a plug. When I eat, it goes pretty much right through -- some foods faster than others. But all that said, I have had absolutely no problems. I agree with Bill about using the bag instead of the plug. I actually take the little bottles of water they give you on the flights into the bathroom with me or have an empty bottle in my carry-on (purchased after security of course) ... and I use water to rinse out my bag as I empty it and also to ensure that I can clean out any "residue" left in the toilet on the plane since there is next to nothing water in the toilets in their lavatories.
As far as security, I have found that if you go through the "walk-through" scanners, the one where it is just walking through, no stop and get scanned ... it doesn't pick up a thing as far as your ostomy appliance goes. The one where you stand with your hands over your head, that will pick up the bag, whether it has anything in it or not. So I do not say a word or show the travel card unless I am going through the scanner where you stand still. Never have had a problem.
So like I said, I love to travel and actually now that I have my ileostomy and am not bothered with Crohn's/UC, I can travel with more confidence than I have in the past. I had my surgery in 2015 and wish I had had it quite a few years before ... but it is all good now, and that is what really counts.
Travel on!
Paula