Custom Icon Compatibility
NightLight's screenshot-based stats rely on an image recognition system to identify loadouts and other information. This system requires training to teach it which icon to associate with which perk, item, offering and so on (much like how we have to familiarise ourselves with them).
The training process involves curating a number of examples of each icon before running a time-consuming training algorithm to teach it what each looks like.
You might see where this is going - icon packs, by their very nature, change the look and therefore won't match what the system knows.
As there are effectively infinite possibilities for icon packs (including ones which randomise the icons...), it's just not practical to train the system for everything.
Functional Middle-ground
As each icon's "chalk" foreground is what contains the identifying information, the system knows to not overly care about the backgrounds.
This means that packs that keep the default foregrounds (or have ones which are very similar) will likely still work.
Recognition performance may well be impacted, but this can be minimised by picking icons with a good contrast between the default foregrounds and their custom backgrounds.
Ultimately, the best way to tell how a pack will perform is to just give it a try.
Not-So-Practical "Proper" Solution
To solve this "properly" (a funny concept given this whole system is a workaround), it would need to be trained specifically for each pack, but they can be mixed or on different versions. Realistically, it would need to go a step further and function on each combination of icons which means per user, and that info would have to be recorded for each screenshot to make training possible.
There would then need to be a system to mass train models that would then have to be dynamically loaded for each screenshot upload...
Admittedly, it's a fascinating task, and one I have given a lot of thought to. However, there are frankly just many easier, more impactful things to spend time on; NightLight is just something I work on for fun in my spare time after all. (Besides, have you seen hardware prices lately?!)