Do that twice, running two firefoxes using two profiles, then click a link in a third application. This tends to try to launch a third firefox process which hangs for a while then says "application already running".
Okay, so you run one of them without no-remote. I had some issues with that, but it mostly works. Now how do you change the default profile? You completely stop firefox, update your shortcuts and finally, in my case, give up on using multiple profiles with firefox on a day to day basis.
I agree this is a pain point when using multiple profiles, and something Firefox should improve.
However it's not a huge issue. Mostly just copy-pasting links from mails etc instead of clicking, which gives the nice benefit of observing which site exactly you're about to visit.
That button grays out when both profiles are running. Try it.
Also if the firefox instance is launched with no-remote, this won't even work as expected. Instead it'll start another firefox instance with remoting enabled, which will fail to start because the profile is already in use.
EDIT: or, to bring up the profile manager:
firefox -P -no-remote