It's hard to say, there's evidence some are carcinogenic. E.g. formaldehyde.

Studies are lacking, so I prefer to err on the safe side. Especially since buying natural furniture that releases less VOCs is not limiting. In fact, it will last longer as materials are of higher quality.

The limiting factor is they cost a lot more than most people can afford.

If you shop around, there are some really affordable options.

IKEA has a whole range of raw solid pine furniture (without stain) that is incredibly cheap. E.g. an Ingo dining table costs ~$50. Last time I checked, it was manufactured in Poland, and it's pretty awesome quality for the price.

On top of that IKEA often has several of the best ranked air filtering plants from NASA's study available at great prices.

Buying used is definitely a good option for well-built furniture. (Here you can get a lot of things for free as well if you're willing to arrange transport.)

If you buy used, VOC's don't really matter. They've already mostly offgassed in someone else's house.