A recent support document on Apple's website confirms that you don't need one of Apple's USB-C power adapters to fast charge the latest iPhones.
Apple says the iPhone 8 and iPhone 8 Plus, and presumably the iPhone X, can be fast charged with any comparable third-party USB-C power adapter that supports the USB Power Delivery specification.
An official Lightning to USB-C cable is still needed, and it's not included with any iPhone. Apple charges $25 for a one meter cable, and $35 for a two meter cable, in the United States. There aren't any MFi-certified alternatives yet.
Apple's own USB-C power adapters that support USB-C Power Delivery include:
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