Firefox, two Linux machines, one X-server

Distinct Firefox instances (eg created with --no-remote) must have separate profiles.

Option 1: Create two (or more) profiles, one for each system running Firefox. Example

firefox --no-remote -CreateProfile localuser
firefox --no-remote -CreateProfile host2

Now start firefox and select a profile at startup

firefox --no-remote -P localuser

or

firefox --no-remote -P host1

Option 2: Set up dynamic solution to create a "disposable" profile on startup, eg a scrupt along the lines of:

TEMPPROFILE=$(date +%Y%m%d%H%M%S)
firefox --no-remote -CreateProfile $TEMPPROFILE 2>/tmp/.mozprofile.$TEMPPROFILE
firefox --no-remote -P $TEMPPROFILE

You may want to add steps to remove the temporary profile afterwards (The direcotry to remove can be found by parsing the output from the CreateProfile command, stored via the above command in /tmp/.mozprofile.$TEMPPROFILE