When we can no longer breed with them ie no mules either.

Read Ray Bradbury's "Martian Chronicles".

It's not feasible for anything but science and/or possibly to mine its resources. What other point is there when there's no atmosphere or significant water to have multitudes taken there, which is also economically impracticable. That goes doubly or more for mars which is some 3+ months travel time one way. PS: what would happen to the balance of the moon to the earth if after 50 or a hundred(s) yrs of transfer of materials. Will or could it upset the tides or other factors the moon is responsible for?

Ahhh..they'll still be human..

Speciation takes many generations of evolution in isolation, to the point of DNA being incompatible with other human populations, so probably thousands of years.

Class them as another species when they become e another species, that's what I say.

Your question is moot. The nature of lunar dust makes the possibility of human colonization unlikely.

So what you are all saying is it just boils down to sex and there's no chance of breeding super mutant humans ???

I would imagine that the separation and differing environmental pressures would encourage the diversion of species. I would say that any differing physical characteristics based on these environments would constitute a different species as soon as there is divergent genetics from the baseline. That base line being the point at which the species separated. Awesome question! I'm not sure if I'm right, but based on my understanding of evolution I would guess that I'm accurate to a small margin of error.

Once the two populations can no longer breed together.

The usual definition given for species is a group of organisms in which two individuals can produce fertile offspring (this definition doesn't always work, though; it's very much a "best fit" ) - so, until our lunar and martian cousins evolve away from those of us back here on Earth to such an extent that we can no longer do this, we'll be the same species.

Depends on what you consider a species. A definite border might be when the core population fails to reproduce fertile offspring with the divergent branch. The first thing that's going to affect these populations is gravity. What that's going to do to egg viability or sperm motility has yet to be determined. But the possibility of humans developing into a ring species will depend solidly on isolation.

I really hope humanity becomes extinct before it starts spreading itself to other planets.

We don't necessarily need to move to the moon or Mars to eventually become a distinct species from what we are now. Consider that our ancestors weren't always homo sapiens but evolved from something before that. In any case, moving off the Earth does not automatically make us a different species, just a resident of a different place.

Only if earthlings can no longer breed with them and produce viable offspring. Very unlikely considering that humans from the America’s and from Europe could still breed and produce viable offspring despite being genetically separated for generations