Can't add ACR Profile to DJI DNG

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"custom ACR Color Profile"

To avoid more confusion, we need to use Adobe's precise terminology.  By "custom ACR color profile", do you mean an "enhanced profile" that you created in Camera Raw, which is stored in a .xmp file and appears in the Profile Browser of the Basic panel in Develop?

Assuming that is the case, then continuing to test my understanding:

"apply my Profile (saved as a Develop Preset)"

So you applied the enhanced profile to a photo and then created presets with the option Treatment & Profile checked:

"the presets containing my ACR Profile are greyed out."

When a preset appears greyed out in the Presets panel, that indicates it refers to a camera profile or enhanced profile that won't work the current photo.  

"no trouble applying my custom ACR Color Profile to Fuji or Canon (or any camera)"

This suggests that you created your enhanced profile in Camera Raw based upon one of the Adobe profiles, e.g. Adobe Color or Adobe Standard. These profiles are defined for all cameras that appear on the Supported Cameras list, which is why your preset and enhanced profile work with your Fuji and Canon raws.

But the Adobe profiles don't work with cameras not on the Supported Cameras list (which is partly what it means to be supported).   So any preset referring to an enhanced profile based upon an Adobe profile will be greyed out in the Presets panel when you've selected a photo from an unsupported camera.

Many DJI cameras are not supported, though because they record their raws in DNG format, LR can still edit them.  To see if your DNG is from a supported DJI camera, select it in Develop, click Reset, and look at Profile at the top of the Basic panel:

If the current profile is Color, and there are no Adobe profiles in the drop-down menu when you click it, that means that camera is unsupported. Because it's DNG, you can freely edit it as a raw, but you won't have any Adobe color profiles to apply to it.

(Note that DJI is very unfriendly and records its internal camera names in the EXIF metadata rather than the product name, and they don't even bother to provide the mapping from internal names to product names on their web site.)

To see the profile to which your preset is referring, click on that preset in the Preset panel (even though it is greyed out) and look at the Profile dropdown:

In this example, I've applied a preset that refers to the enhanced profile My Enhanced Profile, which was based on Adobe Standard (note that Adobe Color and most other Adobe profiles are based on Adobe Standard).

The Basic panel shows "Profile: Adobe Standard" and "! Profile missing", which indicates there is no Adobe Standard profile defined for the camera of the current photo (because the camera is unsupported).

I don't understand your question. You can't save a profile as a preset, so what exactly are you trying to do? If you mean you saved a preset that applies a profile, then do remember that profiles can be camera specific. A preset that applies a Fuji or Canon specific profile is not compatible (and so it will be greyed out) with DNG files from a DJI drone.