I’m not sure you’re right there.

Co2 is released in the production of cement (in cement factories). Once it’s used in the buildings it actually sucks back some of that co2 back during the first years.

In biosphere cement was actually a carbon sink, but it threw the system off balance, because it caused bacteria to eat more oxygen than expected.

https://apnews.com/article/56b7e682362016c1d97f094c2cde4a46

Sorry for the tangential drift but it's ubiquitous now. I guess those boring grammar pedants should finally give up. The totally meaningless and incorrect apostrophe in it's (unless it indicates an abbreviation) has gone viral. You can even find it in headlines in newspapers. Odd really that many of us go to the trouble of adding a pointless character intent as we are on writing correct English. I think we should keep on trying though.

I suspect a lot of the rise is fueled by autocorrupt on smartphones. It changes every damn time on iPhone, and it takes effort to get it with no apostrophe.

The English language changes over time.

Why would a moonbase need to be a closed system? What would stop it scrubbing the CO2 and venting it in to space?

Does the vacuum of space generally require a closed system? And venting the CO2 is bad for the same reason that the heat death of the universe is bad; at some point you have converted all of the usable stuff into useless stuff and have vented it somewhere that you will be unlikely or impossible to be able to recover it.

If we do that, we will have to resupply the O2 in some way other than converting CO2 back to oxygen. Either shipping new gas to the moonbase, or having the moonbase convert organic material on the moon to O2 (which sounds a lot more expensive and difficult than having plants scrub CO2 into O2 for us).

This is also not to mention the other valuable things were venting with the CO2 (heat for one; I assume keeping a moonbase at a livable temperature would be a struggle). Your scrubber also has to be able to replenish the gas while it's venting, or you risk having rapidly fluctuating pressures in the moonbase. Which is going to be uncomfortable for living things, and will require whatever the moonbase is made out of to be able to handle those changes in pressure (again, I imagine having pressure that fluctuates like a bounce house with a group of sugared up children in it is less than ideal). It's not hard to imagine a non-rigid structure like the base from The Martian bouncing off the surface of the moon when it rapidly constricts from venting CO2 and then rapidly inflates as the O2 replenisher kicks on. It would become a massive bouncy ball in 0G.

Eventually, you could convert all O2 to CO2 and be left with nothing?

I don’t think it’s clear at all that concrete wouldn’t work for a moon base. I can definitely at least imagine that there might be some CO2-scrubbing technology that might be practical on the scale of a moon base that wouldn’t be if scaled up to the entire planet Earth.

The good news is that there's very little calcium carbonate on the moon, so you'll have to build it out of something else. Probably thermally fused silicates.