It's been discovered that Amazon's Prime Exclusive Moto G4 doesn't have an unlockable bootloader, as Motorola lists this detail on the support page for their bootloader unlock program. Once the Moto G4 was officially made available for purchase in the U.S., it was quickly noticed that Amazon would be selling a Prime Exclusive model of the device, although at the time it wasn't known that the bootloader couldn't be unlocked. The phone in question, comes with the same Android 6.0 software as other Moto G4 units, but it also carries Amazon ads and a suite of Amazon's applications built in. This is likely the reason for the lock on the bootloader and the lack of a way to unlock it, and the additional software is also the reason why Amazon was offering it for $50 cheaper than the standard model like the one you could buy straight from Motorola.
While Motorola's reasoning behind not supporting the unlock codes for the bootloader makes sense, it somewhat leaves consumers in the lurch who may have purchased the cheaper model to save some money and are also fans of rooting devices and flashing custom firmware. Having said that, it's entirely possible that the development community will find a way to unlock the bootloader on their own and make the information public, although users should not bank on that scenario, and may want to consider the standard model of the device if they have not yet bought the phone.
Hopefully not too many consumers have purchased the Prime Exclusive model envisioning they would be able to grab a bootloader unlock code down the line as they will be sorely out of luck. Of course, consumers could also opt to buy the Moto G4 Plus instead, which does come with an unlockable bootloader and can also be purchased from Amazon, albeit without a Prime Exclusive status. Those who do get either version of the new Moto G and are able to get the bootloader unlocked, will be able to flash TWRP to the device which will allow them to move further by throwing on a custom ROM once they become available to download and install.