(If you don't, you can stop reading.)
These errors happen because Chrome and Chromium try to use the same user data directory. You'll also encounter them if you install multiple channels (stable, beta, dev) side-by-side.
Starting in M61 (now in stable), Chrome understands a new environment variable that enables a solution to this problem. To use it, create a file ~/.chrome-remote-desktop-session with the following contents. (If you already have this file, just add the first two lines at the top.)
export CHROME_CONFIG_HOME="$HOME/.config/chrome-remote-desktop/chrome-config"
unset CHROME_USER_DATA_DIR
. /etc/chrome-remote-desktop-session
Then restart the host by running:
/etc/init.d/chrome-remote-desktop restart
Now Chrome stable, Chrome beta, Chrome dev, and local Chromium builds can all run side-by-side within CRD, just as they've always done (well, for a long time at least) outside CRD.
(Warning: you'll get a fresh profile when you make this change, which is why we haven't made this the default configuration. See
crbug.com/726016 for more discussion.)
Steve