Pictures uploaded to Facebook display wrong colors, but only in Firefox

A bit of Googling finds that colour management is switched off by default in Firefox [I'm not even going to comment on what I think of that idea;)

To enable it...

1. type about:config in the address bar & hit Enter.
2. It warns you you're going into some 'advanced' mode, accept.
3. Type gfx in the search bar that appears.
4. Scroll down until you find gfx.color_management.enablev4 & click the icon to the right to set it to true
5. Below that, set gfx.color_management.mode to 1 by clicking on the pencil icon
6. Leave force srgb at false & rendering intent at 0

You should end up with this…

Quit & relaunch.

Tadaahhh!

Essentially, using those settings means it will use the embedded profile if there is one, or assume sRGB if there isn't - which is about as sensible as you can get for untagged files.

From comments
I can't test this absolutely 'fresh' on Mac as I have had Firefox installed for a long time - though I have never really used it & certainly never set up management before - so I'd think off is default.
On Windows 10 with a brand new install, never before seen on that machine - default is definitely off.

According to ICC color correction in Firefox, Firefox has been capable of reading colour profiles in images since Firefox version 3 (released 17 June, 2008). This was configurable, and initially defaulted to 'off', but this default behaviour was changed to 'on' in Firefox 3.5 (released 30 June, 2009).

However, this comes with a big caveat. It seems ICC profiles come in two versions, and Firefox only reads the older version by default. Quoting Wikipedia, "Two main generations are used: the legacy ICCv2 and the December 2001 ICCv4. Since late 2010, the current version of the format specification (ICC.1) is 4.3."

There is a configuration setting to get Firefox to read ICCv4 profiles. To enable this, enter about:config in the navigation bar, and search for and change the setting gfx.color_management.enablev4.

As mentioned by the OP, this is all well and good for your own browsing experience, but it's quite unlikely that other Firefox users will have gone and fixed this configuration themselves. It looks like there is some ongoing work to address this by Firefox developers, but since the linked bug is 13 years old and still open, I wouldn't hold your breath. If you want to fix this yourself for all Firefox users, here's how to contribute to the Firefox code base: https://developer.mozilla.org/en-US/docs/Mozilla/Developer_guide/Introduction