When tmux's mouse support is enabled (via
set -g mouse on), clicking in a window pane will trigger tmux's copy mode, which is not what you always need. To select the text as you'd usually do in rxvt-unicode, one can temporarily disable mouse reporting by holding down the shift key before clicking using the left mouse button.
After upgrading to Ubuntu 16.04, which has rxvt-unicode v9.21 and tmux v2.1, it seems like disabling mouse reporting is broken. Even after pressing down the shift key, mouse events are being sent to tmux and tmux's copy mode and a conventional rxvt-unicode selection are both triggered simultaneously (in response, the selection flickers a bit).
I tried several things (including patching rxvt-unicode using this patch), but I'm not able to get the expected behavior. I believe this problem is rxvt-unicode centric since other terminal emulators (xterm, xfce4-terminal, gnome-terminal, etc.) work as expected. Is there a way to get around this issue in rxvt-unicode?
EDIT On further investigation, I found that this is no longer an issue with the rxvt-unicode package (v9.22) shipped with Ubuntu 16.10. So this was either fixed between versions 9.21 and 9.22 or there is some problem with the version in Ubuntu 16.04.