you're running multiple profiles of Firefox at the same time (so restarting one with a queued update writes the changes to disk, throwing the other profile instances out of alignment).
In that case, launching a different profile in a new window should not use the new version. In other words, Firefox should not do anything with the pending version until the user actually restarts the entire browser. Having the second window run in the new version just because there was a pending version seems like a bad approach.
The problem is that the user should not be prevented from browsing the web just because a new update is ready. The user should choose when to update. If the user has multiple important tabs open, they should be able to finish their work, but if Firefox refuses to load any new tabs, then the user cannot continue working normally.
But if the program isn't restarted then it could become unstable or crash. You shouldn't really have any software running while doing updates anyway. I browse the web knowing that I'll need to restart Firefox so I never do anything of import while waiting.