The actual script is as follows

#!/bin/bash

export MOZILLA_FIVE_HOME="/home/kristianf/Applications/firefox/current"

url="$1"
if [ "x$url" = "x" ]; then
url="about:blank"
else
url=http://${url##http://};
url=${url/http:\/\/https:\/\//https:\/\/}
fi

if $MOZILLA_FIVE_HOME/mozilla-xremote-client -a openURL\("$url"\); then
exit 0
fi
exec $MOZILLA_FIVE_HOME/firefox "$url"

How to use it

Mozilla Thunderbird

user_pref("network.protocol-handler.app.http","/home/kristianf/Applications/firefox_remote.sh");
user_pref("network.protocol-handler.app.https","/home/kristianf/Applications/firefox_remote.sh");

If you don't have this file in your profile directory, then create it. it itsn't there by default. As you see this file set a new protocol handeler, in this case to a shell-script making use of Mozilla's xremote procedure. The shell-script in my case look like:

X-Chat

To use it from X-Chat you would add the following to urlhandlers.conf

NAME Browser
CMD !/home/kristianf/Applications/firefox_remote.sh "%s"

As always, comments and how to do it in other applications as well are welcome.