(On Windows anyway, don't know if different on Linux)
Just wanted to share that as a user of both Firefox and Chrome, it's one thing that makes me hate switching to Firefox. I often need to use two different profiles and the way Firefox does it sucks.
With Chrome I've got two shortcuts (that Chrome creates by activating an option) pinned to my taskbar that look distinct from one another and the instances that I open are combined under their respective profile shortcuts.
With Firefox I need to manually create two shortcuts, assign two distinct icons to differentiate them, change some properties so they open the right profile, pin them and because they're "regular shortcuts" instead of the default Firefox launcher shortcut, when I open the program I end up with a third Firefox icon in my taskbar (it does not open under the shortcut I used, it acts as if I clicked a shortcut on my desktop) where all instances get merged together no matter which profile they're associated with.
I think the few times that happens it's the first profile that has priority, in our case it doesn't really matter as it's only game launchers under my name that do that anyway.
We also have other computers just for our own stuff, it's the one connected to the TV where it's an issue.
Okay, since it doesn't like it's your main computer or anything, you might be interested to try taskbar profile grouping. Go to about:config and while there create a new boolean pref named
taskbar.grouping.useprofileand set it totrue. Doing that the two profiles should have their own group in taskbar. It's a very crude feature though, since for example the right-click jump list items are not separate and you can't set different icons for them (unless you do that via Windows somehow), but it sort of works.