> Hydrogen and oxygen can be made from water

Judging by [this][1], good luck trying to find adequate supplies of water on the Moon.

> methane can be made from regolith and water.

Again, good luck with that, because as shown [here][2], the amount of carbon in the lunar soil is, shall we say, not great. And since we are already talking about an immensely energy intensive process here, breaking down rocks in a smelter to get at tiny amounts of Carbon, may not be a very good solution.

So to have a chance at an adequate supply of CO_2 for the Sabbatier Process, you'd have to mine cold-trapped carbon dioxide. Which [may exist][3], or it might not. If it exists, it exists in the coldest regions of the moon, aka. places where you have no access to the only available energy source (Solar). Good luck hauling dry ice across the Moon to the base, especially since it will cease to be a solid the closer the transport comes to the processing plant.

And this process btw. requires HUGE amounts of energy, equipment, machinery and storage infrastructure. [This video][4] gives you a good idea of how difficult making CH_4/LOX fuel with ISRU using the Sabbatier process is ... on Mars, where you can actually pull CO_2 from the thin atmosphere, and likely have more water available.

So in summary:

1. No, we cannot just make the fuel on the Moon

2. Even if we could, it would likely end up being comparatively easier to just ship it there from Earth

3. Even ignoring all that, good luck making the amounts required to keep industrial-scale launches of materials happen

> control for foreign material

If you want to have a real challenge regarding keeping foreign material out, then try manufacturing things in an environment that is filled with hyperstatic, completely dry, microabrasive, pulverized regolith, and having to build clean rooms in an environment with the kind of temperature differentials experienced between the lunar day/night cycle, or worse, in space.

Also, if a clean room fails here on Earth, it's a huge headache for everyone to recover it. If an airlock fails on the Moon, people die, and the production facility gets destroyed by explosive decompression.

> And they will be cheaper in space, and on the moon and mars.

No, they won't, because again: These materials, even if they actually benefited from being produced off-world (and that's a big IF) will only be of any use here on Earth. There won't be any self-sustaining colonies in outer space, or on the Moon, or on Mars. There won't be sprawling industrial sites. We'll be lucky if we can keep a small crew of Astronauts alive on another Planet or the Moon for a few Months until they can get back and start the recovery process after having their bodies wrecked by Microgravity for a prolonged period of time.

So the only market for ANYTHING produced "up there", is "down here", and this, again, is where the prohibitive transportation costs come in and make the whole discussion moot.

[1]: https://en.wikipedia.org/wiki/Lunar_water

[2]: https://en.wikipedia.org/wiki/Lunar_soil#/media/File:Composi...

[3]: https://www.sciencedaily.com/releases/2021/11/211115151010.h...

[4]: https://www.youtube.com/watch?v=Wum8_8sWdeU