The Nexus 5X and Nexus 6P don't support aptX Bluetooth streaming capabilities according to an official Google employee as it was recently noted on the Google Issue Tracker. This was a response to an issue/bug post that was created by a user of the Nexus 6P, who reported the problem as a bug that they noticed following the installation of the latest Android O Developer Preview software. While it may have seemed like just another problem that was hitting the device due to beta version software and which could potentially be fixed once a final version of Android O is rolled out, that now doesn't seem to be the case.
According to the Google employee who responded, the bug was marked as "won't fix" and is only available on newer devices, which will mean the Google Pixel and Pixel XL, as well as future devices put out by Google, and other newer devices from other manufacturers. Though this is probably frustrating for some users just for the sheer fact that it isn't supported, what might make it more frustrating is that some devices which are older than the Nexus 5X and Nexus 6P by a small margin do support aptX Bluetooth streaming, such as the LG G4.
Unfortunately, it also isn't made clear what the requirements are for aptX Bluetooth streaming to be supported. So it could simply come down to not having the necessary hardware components, or it could be that Google may not see the need to update the Nexus 5X and Nexus 6P to support this Bluetooth feature. It could also be a combination of not having the necessary hardware and firmware. Whatever the reason, it seems very much likely that Google is going to stand firm on this matter. That said it is worth keeping in mind that Google could always change its stance and look into whether or not adding aptX Bluetooth streaming support is viable, as it did something similar with the Nexus 5X and Nexus 6P in regards to the fingerprint gestures that came with the Pixel and Pixel XL, first stating that this feature wouldn't be supported, then finally deciding to enable it with the Android 7.1.2 Nougat update that was pushed out to each of those two devices. In any case, if you were hoping for aptX Bluetooth streaming to come to your Nexus 5X or Nexus 6P, it looks like it's not happening.