I would like to pull this card out in a tabletop game however. Imagine the characters have been invoved in even a small skirmish on the road and a couple days later they come to a town. The town watch would ask them where they were coming from and how they found the roads and then specifically ask about the bloodstains on their cloaks. It's not like they have changed or stopped at the river to wash.
"Why officer we are a band of minstrels coming to town to participate in the autumn festival. Blood? What? You want to look in the saddlebags?"Also blood (not to mention sword and arrow tears, scorch marks and all the other things you might come across in a fantasy world combat) would probably be pretty hard to wash out. I would imagine the party looks pretty messy, and in a dangerous way that would get you reported to the neighborhood watch if you were walking around civilized folks. Yes everyone is dirty but they are mostly covered in shit, not blood and brains. If they are actually coming back from a dungeon then it would be like 50 times worse - they should be lucky if they even have clothes. Try playing out a scene where the characters slip off to an underground lair and then have to pop in for tea at the magistrates house.