Hard to say exactly without seeing the actual files, but it sounds like browser variations in the way that ICC color profiles are being handled. More details on FireFox specifically over here. But it might not be FireFox being the problem & more connected to whatever your main development browser is & how it handles ICC profiles as well.
Like the FireFox article implies, the feature is fairly old in many browsers but what I have noticed is many modern browsers nowadays are actually paying attention to ICC profiles as a default, whereas before that feature was disabled by default.
Which is all to say I would see how these images look if you strip out all EXIF metadata using a tool like exiftool. Without an embedded ICC color profile, the images should render similarly between all browsers.
And to strip out all metadata with exiftool
you would just run a command like this; assuming your file is named test.jpg
:
exiftool -all= test.jpg
You will end up with a backup file tagged as test.jpg_original
that still has EXIF data embedded and a cleaned test.jpg
that now is 100% stripped of EXIF data.