A dry atmosphere is full of nano-particles (and yes they are harmful). But natural particles tend to be larger and more benign than most human made ones.
Nature copes with them the same way it copes with ever other long term problem: it affects individuals, and individuals are all dead at the long term anyway.
Well, fire is the really obvious one. I'd be very surprised if these put out more than a charcoal grill, much less a campfire. But of course everybody understands the need for proper ventilation when using one of those.
Volcanic ash or, more topically, wildfires are some more good examples.
I'm not sure what you mean by "cope". There's so many things that are nature, and many are entirely unaffected while others are irreparably affected immediately. If you kill off a whole bunch of prey animals all at once you might see a decline in predators, a simultaneous explosion of scavengers, and then a correction as the predators switch to the scavengers as their primary prey. Or you might see a complete ecosystem collapse. Natural systems are so many things from the water cycle to the flora and fauna to the geological systems.
"Cope" here is "how we are not dying from them". Either our bodies have adapted to some nanoparticles (mineral, but not plastic yet), or we're far enough away that the natural particles get absorbed by e.g. ocean waters or soil and don't readily get into our lungs.
Another case, which I totally overlooked, is pollen and dust, which do result in serious negative reactions in humans, quite regularly. This may be not outright deadly but debilitating nevertheless.
Short answer: we don't. You breath enough smoke, it kills you, you die in part because these nano-particles (soot) are clogging up your lungs (Along with the CO2/lack of O2). Carbon particles in your food are carcinogenic and can accumulate in your body. Everything around you is constantly killing you by inches. Your body is pretty good at just ignoring anything that isn't causing immediate system shocks and allowing you to function.
Which is to say, the fact that toxic particles are being spewed by your 3D printer might not be any worse than working next to a grill. That's not to say that either is good, and you should probably minimize contact to prevent accumulation. We haven't "adapted" to natural chemicals, it's more that different chemicals are different degrees of problematic to the body.
