If we start mining the moon, surely we're just going to eat up all the resources there and maybe cause lasting damage?

It's a hard one to call but the Earth is a relative paradise compared to the moon so if we can help save the bio diversity on the Earth by exploiting the moon I think there is a strong argument for us doing it. If however we just end up exploiting both and being even more wasteful then we would be better off leaving it alone.

I think if we're going to invade Mars, we need to exploit the Moon for everything it's got. We are going to invade Mars aren't we?

The moon serves as a dead weight allowing tidal forces to operate on earth, nothing more. Not only should we take whatever we need from the moon, we should do it as soon as we possibly can. The less we have to tear up on earth the better.

Were gonna go to mars right? were going to need resouces + who cares about the moon? what'll happen to the moon will we hurt its feelings?
I say go ahead and mine the moon mars or no mars

There are too many choices:
1) Not mining moon resources -> Continue burning coal to warm the Earth -> We all die. => Mining the Moon

2) Mining moon resources -> Power the Earth by helium and have enough nuclear power to travel to the other side of galaxy -> meet some advanced aliens -> here there are new choices.
a- Greet them -> They give green technique / tech that will help recycle energy / prevent energy losing in heat form. => Should mine the Moon.
b- If they're too aggressive + advanced -> We all dead => Not go to Moon.

3) If there're going to be enormous amount of Helium on Moon -> One mistake / someone might activate accidentally / purposely the nuclear reaction chain on the Moon. => All dead => Shouldn't mine the Moon.

This gives me the best choice of all: Another enormous asteroid will strike the Earth next month. -> We might all die (or at least the ones who know how to make space shuttles / to activate nuclear reaction, will die) -> Can't go to the Moon = end of story as no mining whatsoever.