OK OK, this is cheating a bit. Wine can run Firefox for Windows on Linux (if you disable multiprocess in Firefox; if you don't, Firefox starts up but nothing will load). rr can run Wine. Transitivity holds.
Caveats: it's slow (rr's syscall buffering optimization is mostly disabled by Wine), and the debugging experience is pretty much nonexistent since gdb doesn't know what's going on. But hey.