Well, that's not what happened with me.. And sure, i don't mind in certain missions. But asside from those i want them to wear what i picked out.
Strangly, the hair i picked remained throughout the game.
Yeah the hair won't change.
How or when did clothes change for you in a different way?
I can probably help make it easier for you to do that if I know how it's happening for you.... I've beat the game 10 times now and I can pretty reliable and easily keep my characters always wearing the clothes I want during missions (it's also very important to me) so if I know what trouble you're having, I can probably explain how to avoid it.
It would definitely be nice if they didn't randomly change their clothes. I'll have Franklin dressed looking good then switch to Michael and find him in a generic outfit. Play with him for a while before switching to Franklin and finding that he too got put into a generic outfit.
I want it like Online where I know what my character is going to look like (not to mention, where I can choose what car I want to use, I can't stand Franklin's car or motorcycle).
Usually when a Switch Scene has a scripted outfit, it's not a specific outfit but rather a type of outfit...
for example, the Switch Scene where F is in his closest looking happy will always have a shirt (with a long sleeve underneeth) and jeans with boots... but all 3 of these are random. So, it'll only use your generic default outfit if you don't any other clothes. Otherwise, it's random. The 'drunk' ones at a store will usually use a t-shirt, at a club or coffee shop it'll be a tight long sleeve shirt, and if at the Unicorn it will always be a shirt with suit pants (or jeans if there are not suit pants). Same for the other characters. Certain 'rejected from a restaurant/club' scenes for T will always have a checkered shirt; same for M's 'at home watching movies by himself. At home with the kids, it'll always be a suit. Et cetera. But in every case, the outfit is random from that clothing type. So, if you have multiple shirts, the shirt can be different every time. If you have different suits, the suits can also be different and they blazer and trousers can even mix and match.
There's very few scenes that always use the exact same outfit. Even most of the drunk T ones technically can have different pants or shorts.
I've tested most of these extensively for video and faq reasons (I've seen every Switch Scene at least 20 times or so) so I can help out with any questions regarding clothing switching outside of the closest. I know which missions let you use other cars, too, since that's sometimes annoying to deal with because some will always spawn your personal vehicle, others will not, and some like Crystal Maze you need to use a trick to get your vehicle to not despawn.