You Can’t Take it With You
So if the stone can only affect living cells, then when they translate those things out be left behind. Which would mean that no clothes, hair, etc. and that’s not good. So let’s say the invulnerability only affects infected cells, but that translation affects anything within a certain radious of an infect cell — as long as the item is not living.
So clothing would stay, but an uninfected person wouldn’t. Of course, you wouldn’t want people taking buildings with them, so it would have to have a small radius. You might end up taking a few bricks, or a chunk of the plaster, but not the whole wall.
This would mean that the Travelers travel light. They’d keep only what they were wearing at the time, or that they had loaded on pack animals. The small radius means no carts or carriages, so most of the travel would be by foot or mounted.
This would also mean that it would be impossible to catch a traveler. If you tied them up, they’d take the ropes with them. If you tried to hold onto them, they’d just pop out of existence.
they also would be less materialistic, but more prone to wearing their wealth. Lots of jewelry that can be traded no matter what the world.
Housing would be things that are easily carried, fabric for tents that would be made from local woods. Whatever they wore would also be archaic or otherworldly, which would add to the legends that they weren’t human.
Lots of superstitions about them
They steal people – which is true, if they touch the stone
They steal children – which is sometimes true, if they need the new blood to keep the tribe going
They are immortal – which is false, but they are impervious to harm from most sources
They are nonhuman – which is false
They are uncreative – not true, they just don’t have a lot of trappings, so they have primarily portable skills
They live in Sídhe/Neverland/etc – false, but understandable, as they reappear at random intervals, but normally once every generation or so
They are scam artists – to some extent, selling Traveling horses is a good way to make money if you need it
They are blood drinkers/vampires/canibals – if we go with the ‘infect the food before eating it’ theory…
They can only be killed by -blank- weapon – which is only partially true, as only travelers from the world the sword is from can be killed by it
Stonebearer – because you can’t have a story without a magic plot coupon
Warrior Person – in charge of guarding the Stone bearer
Animal Handler – because every story needs a Goose Girl
Main Band is about thirty people (eight families), forty-odd horses, twelve dogs, a small group of sheep and goats,