That's a very good question and one I've thought about over the years.
Let me first say that, what I've found about myself when doing any of the handful of "diaper excursions" I've done over the years is that the longer I'm out in my diapers, the more brave I get. I'll start off being very careful then slowly make them more obvious, for instance, instead of letting my t-shirt cover my plastic pants I'll reach around back and actually pull up the plastic pants and tuck the bottom of the t-shirt in them to make them totally obvious. Also, since I wear thick cloth diapers, the more they get wet the more they sag, making them even more obvious. On a few of these occasions I've actually pulled off my shorts and gotten out of the car to get gas, mail a letter, buy a drink out of a machine, and such while only in a t-shirt and diapers/plastic pants.
And on a few occasions I've been caught this way. The most memorable were at gas stations. Once I was putting gas in the car--nothing but a t-shirt/very wet diapers and plastic pants--when the young, pretty attendant (probably 25, blonde and a bit on the "pleasingly plump" side came out to sweep. As I put the hose / gas cap back and came around the car to get back in it she walked around the gas pumps and saw me--from about 15 feet away--and got this big astonished "I absolutely do not believe this!" grin on her face.
Another time I was doing this and as I was finishing up a girl, probably 18-19, actually walked up to me and asked if I could give her some money for gas, she was from another town about 30 miles away and didn't think that she had enough to get back. This, while I was standing there putting gas in the car wearing nothing but a t-shirt, diapers/plastic pants, and flip flops. I said "Sure" and after finishing with the gas sat down in the car, got out my wallet and handed her a few bucks and she thanked me and went back to her car. That particular day I'd awakened in my very wet overnight diapers, gone out in them that way, wet them a lot more and even done a big poop in them and it was completely obvious--even while I was sitting down because of how the poop stains had made their way around to the front and were plainly visible around my legs.
And what I found was--both times this happened, at the "moment of truth" that I thought would absolutely terrify me and embarrass me to death--what I really experienced was absolute complete joy over the fact that I'd just been seen this way, I was experiencing my fantasy of being seen this way, and I loved every minute of it.
So, that being said, it's hard to know how much embarrassment would be "too much" because once I'm experiencing it, I may love it so much that I'd want even more.
But anyway... Let me describe a situation I've thought about for years and on a few occasions, my wife has actually said that yes, one day maybe we can do this: Book a weekend at some small hotel/motel at the beach with the intention of me spending the entire visit there in diapers.
When checking in we would tell them at the desk that "I'm in diapers, is this going to bother anyone? Tell the maids who service the room about this and that I'll be in there with a diaper pail full of my diapers in the bathroom, just ignore it, it goes with me everywhere. Is there anything you'd like me to do because of this? Plastic liner on the bed? I do not usually leak but can put a pad under me if need be."
Sometimes the maids are young women, this could be lots of fun and very embarrassing just noticing the looks on their faces and hearing anything they may say about it. Often the maids are speaking Spanish and in that case, I'd have no idea what they were talking about (though it might be fun to learn the Spanish words for "baby" and "diapers" so I'd know if they were talking about me).
Checking in / out we'd not at all try to hide the fact that along with the luggage we were taking in a big babyishly-adorned diaper pail and stacks of diapers/plastic pants.
Then in the mornings when they come to service the room I'd just be sitting there in a t-shirt / diapers, like, "everybody knows, not even trying to hide it". We'd get a room with a balcony overlooking the beach and I'd spend much time out there where everyone could see me. And if that went well, maybe we'd even take me out to be beach with them obvious under my shorts (or, perhaps not).
Well, this may never happen but if it ever does, be sure I'll show up here and document the entire experience!