I'm starting this thread because there is a lot of erroneous and outdated information out there regarding this, which people are still to this day having issues with, so instead of repeatedly repeating myself, I can just link people here, or maybe they'll be fortunate enough to happen upon this thread first themselves. Thanks for your understanding. 
Depending on what versions of the game you have installed, there are potentially a few different files in different file locations that you can edit to change your HUD colors. However, there is only one file and file location that is the same throughout, that doesn't need to be reedited after the game is updated or different versions of the game are installed.
Make sure you have your Windows Explorer Folder Options View settings set to show hidden files and folders.
Navigate to this folder and file location. → C:\Users\[Your User Name]\AppData\Local\Frontier Developments\Elite Dangerous\Options\Graphics\GraphicsConfigurationOverride.xml
This file might not yet exist for you, in which case you will need to make it using a basic text editor such as Notepad. If the file does already exists, open it in a program such as Notepad to be able to edit it. Just make sure to save it in the location mentioned above with the same name and to correctly save it as an xml file type.
Here is an example of the contents of this file that I am currently using, which changes the HUD panel colors to light blue, white, and yellow. ↓
You can use this web app to preview what affect changes made to these values will have on the colors of your HUD Panel. → http://arkku.com/elite/hud_editor/
Note that some people have reported having issues in Elite Dangerous: Horizons using negative values where they had previously worked in Elite: Dangerous. I have not tested that myself.
Depending on what versions of the game you have installed, there are potentially a few different files in different file locations that you can edit to change your HUD colors. However, there is only one file and file location that is the same throughout, that doesn't need to be reedited after the game is updated or different versions of the game are installed.
Make sure you have your Windows Explorer Folder Options View settings set to show hidden files and folders.
Navigate to this folder and file location. → C:\Users\[Your User Name]\AppData\Local\Frontier Developments\Elite Dangerous\Options\Graphics\GraphicsConfigurationOverride.xml
This file might not yet exist for you, in which case you will need to make it using a basic text editor such as Notepad. If the file does already exists, open it in a program such as Notepad to be able to edit it. Just make sure to save it in the location mentioned above with the same name and to correctly save it as an xml file type.
Here is an example of the contents of this file that I am currently using, which changes the HUD panel colors to light blue, white, and yellow. ↓
<?xml version="1.0" encoding="UTF-8" ?>
<GraphicsConfig>
<GUIColour>
<Default>
<LocalisationName>Standard</LocalisationName>
<MatrixRed> 0, 0.25, 1 </MatrixRed>
<MatrixGreen> 0, 0.5, 0 </MatrixGreen>
<MatrixBlue> 0.25, 0, 0 </MatrixBlue>
</Default>
</GUIColour>
</GraphicsConfig>
You can use this web app to preview what affect changes made to these values will have on the colors of your HUD Panel. → http://arkku.com/elite/hud_editor/
Note that some people have reported having issues in Elite Dangerous: Horizons using negative values where they had previously worked in Elite: Dangerous. I have not tested that myself.
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