Even if a ship's crew doesn't exert itself too much while onboard, once planetside while adventuring I'd suspect there could be at times a chance to really exert yourself. Also, I'd suspect that having a small laundry on a ship for the crew would give a crew alot more flexibility in allowing you to do your cleaning whenever you want rather than having to take the time when planet side, when you could be out adventuring, etc.
I was mostly speaking to the space travel portion; I assume Scouts in the field would equip themselves appropriately. Then again, Scouts in the field may have less need for uniform changes and more need to carry other supplies. I've done some long distance hiking where a clean change of clothes was the least of my concerns.
In real life I've spent a little time working with small craft test crews as well as doing some ship checks myself, and although you can wear a pair of coveralls (or a flight suit) for a couple days in a row, usually I ended up getting my laundry done once a week.
So you're that guy!?! I know what you mean about wearing coveralls well beyond their intended life span. I've also been so busy onboard ship that laundry was secondary to a long list of other priorities. It's only when you have to wear a pair of socks a second day do you realize you're out.
If you're going to have a short run of 7 to 10 days 99 times out of 100, then you might or might not need the onboard laundry, but if 2 out of 5 trips are longer, then it might be a problem.
I agree, it was a generalization. If a crew expects to be away from civilization for extended periods, then a laundry might be something they want to install in an unused corner. There might be other things as well pertaining to the food and entertainment threads that are running here simultaneously.
There's also going to be issues with accidents ("Oops, I spilled my kung pao chicken in your lap") and with systems that are not completely self-contained ("Cleaning the wastewater filtration units isn't always pleasant"), or just plain malfuctioning ("That actuator was sticking but with my trusty hydrospanner, I showed it who was boss").
I concur, coveralls are meant to get dirty and they don't take up much space. So one set get some gunk all over them; just change. I would assume in the far future there may be something better than stain resistant cloth or Scotch Guard to treat clothing that may alleviate this problem.
Leaving aside issues of just how you "minimize perspiration" for multiple people, there are also personal items of clothing that need to be cleaned on a more frequent basis, such as underwear and socks.
Socks are something I'm sure could be engineered better. I have some wicking socks that seem to reasonably un-scary to wear twice.

But with what I would expect would be the normal evolution of clothing, even better materials would be available.
I think it'll wind up being needful to have some facilities for at least basic cleaning onboard the ship. It doesn't have to be capable of handing every possible insult to every possible garment, but your ship's going to be pretty disgusting if you omit that element.
I have to disagree about the disgusting part. A lot of that is Western perception. There are a number of cultures on this planet where such things are not considered as important as others. It may be shock to cultured Western noses, but it's their norm.
But back to vacc suits and what Travellers wear; what about a body glove under garment for vacc suits that are used to regulate heat and moisture? Like a 2mm wet suit or Under Armor uni. The body glove could be worn around ship, maybe under a flight suit or coveralls, or under a vacc suit, where it performs the previously mentioned function. It could even be worn separate by fit Travellers without much embarassment.