Is there anything special about the Apple USB-C cable, other than its quality, that would prevent me from using a USB-C cable from another brand?
And the same question for the wall adapter.
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The only thing that's 'special' about them is they are MFI-certified from Apple. This means that Apple ensures it will work with all their devices. Third-party accessory makers can also have their products MFI-certified by following the guidelines that Apple publishes.
The question of 'quality' is subjective in that what I think it means might be different than what you think it means. I spent a lot of money on my Apple products so I will only buy MFI accessories (they could cost more money than non-certified products).
In this manner, any USB-C cable will work but it's up to you to decide if a higher-quality cable will give you the piece-of-mind that there's less a chance that the cable will fail or cause other problems for you.
A USB-C cable is a USB-C cable. There's nothing special about it with the exception of quality (which you already mentioned.)
As far as adapters go, there are "genuine" adapters which are actually OEM'ed by a 3rd party company with Apple's blessing and then there are the myriad of knock-offs you can find on Amazon and eBay.
If you are using the USB-C charger/port to charge your device, technically speaking, any cable/adapter will do. That said, when you purchase said cable/adapter, look for quality products, not the cheapest you can find.
What to look for...
USB certified Charger Logo. This means that the charger is USB-IF compliant.
Does this mean that the no-name or off-brand products are bad? No. It means that the manufacturer has taken the time and cost to certify their products to a certain level of quality and performance. (IMO) Saving a few dollars on a cable/charger is simply not worth it when attaching it to a $1000+ Mac that I use for daily work.