So, if you have frequent ships shuttling back and forth to the Moon - then that's an end to our ability to study the Lunar atmosphere in its current relatively untouched state.
So - a matter of priorities there, it's something that needs to be thought about, that's all, don't know what the outcome of that debate would be, but since you asked what the effects would be.
Then, within a few centuries, a thin stable atmosphere would form on the Moon, augmented all the time by the waste gases from mining operations and the ships landing and leaving.
That would be a benefit for colonists as it would reduce the danger from micro-meteorites.
The Moon can't keep an atmosphere for long in geological timescales of millions of years - but it can keep one easily over the shorter human timescales of centuries or millennia.
VULNERABLE AREAS ON THE MOON OF SPECIAL SCIENTIFIC INTEREST
Then - particularly vulnerable areas where you might have conflict of humans with scientific interest:
Caves. There are probably few caves on the Moon, lava tubes. Ideal for humans to shelter from surface conditions. But - doing that will mean they are no longer pristine for scientists who want to study them in their original condition. They may also trap some ice, if so then there are other reasons also for caring about them, see next point.
Trapped ice at the poles. Now - there are likely to be huge amounts of ice. So just removing the ice not likely to have much of an impact on the total amount there or reduce it significantly. Even if using it to supply water to LEO - if they are right about the quantities there - it won't make a significant difference to the amount left for future lunar colonists for a long way into the future.
But - there is the issue of contamination again. The rockets by landing and taking off will contaminate the ice with their exhausts, And humans - would probably leave wastes on the surface, as happened already with Apollo - and bits of organics - e.g. when you vent air from a habitat - microbes and fragments of skin etc. spreading out over the surface of the Moon around the habitat.
The ice at the poles is likely to be of interest for ice cores, a bit like Antarctica - tracing the history of our solar system in the ice of the Moon.
Also - it is likely to include some debris from impacts from the Earth on the Moon - and if you go deep enough - e.g. parts that get covered over by later impacts - maybe have ancient organics from Earth also.
So - scientific potential unknown - but could be of great interest potentially. If that's so we might need to step carefully there.
So again - you'd need to decide what to do about those.
Depends on how important those deposits are scientifically I imagine. If they are like Antarctic ice cores, maybe doesn't matter much if humans walk over and contaminate the surface, what matters is below the surface.
But they might be very important and perhaps the surface deposits also matter - that we need to keep even the top few mms clear of contamination until we can study it properly.
MOON IS A GOOD PLACE TO EXPERIMENT WITH EFFECTS OF HUMAN EXPLORATION ON THE SOLAR SYSTEM
The current Outer Space Treaty requirements for the moon - as interpreted by COSPAR - are not stringent. You are just required to document what you do, so others who follow can take account of that, e.g. if they detect contamination on the Moon they know where it came from.
That's because it's not thought likely to have life there or to be a place that Earth life could reproduce.
Surely more protection will be needed eventually for the more sensitive areas of the Moon.
However, meanwhile, this makes it an ideal place to study the effects of contamination by humans on a solar system body in practice on another solar system body.
This is something you can't do on Mars because the experiment there has a significant risk of irreversibly contaminating Mars.
IS IT POSSIBLE FOR HUMANS TO EXPLORE THE SOLAR SYSTEM WITHOUT SIGNIFICANT CONTAMINATION CONFUSING YOUR STUDIES?
Can humans explore the solar system close up without contaminating it? Or do they always inevitably contaminate everywhere they go hopelessly so that it is best to keep them well away from anywhere at all of scientific interest?
We don't really know for sure. And the Moon is an ideal place to start to find out. With small scale visits - first by machines. Humans landing in less sensitive places similar to the places already visited by Apollo. And then study to see what happens - do the sites they visit get contaminated a lot by rocket exhausts and debris from the habitats (including the various human wastes, and vented gases from the habitat)? Or are they able to contain the contamination?
How far does the zone of contamination spread around a working habitat in lunar conditions after humans have been there for some months or years? And what is it like in practice, what sort of contamination do we see?
We can find that out in the less sensitive places first, and that could inform us about whether humans can or should visit the more sensitive places on the Moon (such as polar ice, and caves) or elsewhere in the solar system.
That includes larger asteroids such as Ceres, comets, Jovian moons like Ganymede or Callisto, the moons of Mars all examples of places of intermediate level a bit like the Moon where humans might or might not be able to explore without too serious contamination depending on what we find on the Moon.
WHAT IF IT TURNS OUT WE CAN'T GO ANYWHERE OF SPECIAL SCIENTIFIC INTEREST IN THE SOLAR SYSTEM WITHOUT CONTAMINATING IT SIGNIFICANTLY?
If it turns out we can't do it with present day technology - you still have telerobotic exploration of sensitive places in the solar system.
We would do that anyway.
Even on the Moon - even if humans were to live there permanently - they might well spend most of their time underground.
The same is probably true of future space stations - instead of sending humans outside to repair them - you would send telerobots - who are not affected by cosmic radiation in the same way. Humans would go outside only rarely, for recreation perhaps - or if they are essential for some reason.
So on the Moon, you'd drive rovers around on the surface via telerobotics - and using telerobots on the surface to do experiments, dig, even for construction of habitats.
That's because humans would want to limit their exposure to cosmic radiation as much as possible - you'd have a maximum lifetime, dose which you'd hit quickly if you spent most of every day on the surface of the Moon protected only by a spacesuit. I'm talking here about people who live on the Moon for long time periods of course, years or decades. Not just a few days in a spacesuit as happened with the Apollo landings.
You'd be keenly aware that if you spent a lot of time on the surface, you have an increased risk of cancer - and early cancer also in this case - high probability that it would reduce your lifespan by a decade or two if you get it - and nothing you can do about it with our present technology (unlike smoking where you can almost immediately reduce the risk by stopping smoking).
So - might not be too onerous to only explore the places of special scientific interest on the Moon via telerobotics - controlled either from underground on theMoon - or from L1 or L2. Might be how we explore the Moon anyway.