It's not trivial to test if having a profile open in a non-MSIX Firefox blocks migration from that profile because of this issue. But I suppose I could run a Firefox Nightly against that profile, which won't be grouped as the MSIX Beta I have installed, to test. If I can work through the profile downgrade issues, which I'm not sure I'll be able to. Maybe if I launch the non-MSIX Firefox with the remote server off I can test this. Yes, that should work. Let me try that now.
Oh dear. If I launch the non-MSIX Firefox with
c:/Program Files/Mozilla Firefox/firefox.exe --no-remote, then the MSIX Beta will indeed launch. Unfortunately, it shows the skeleton UI and then spins for a while, presumably as it tries to lock the default profile in use by the non-MSIX Firefox. It then pops the "Firefox is already running, but is not responding. The old Firefox process must be closed to open a new window." dialog.
This is perhaps not a terrible outcome, though: at least it's clear what the user needs to do to make progress. They may be surprised later to discover that the two can run side-by-side after the initial import, of course. It's probably tricky to make that message say something about profile migration/import, since we might not know we need to do migration/import so early, but we could consider it.