Customization of the variable has no effect as long as python-mode-syntax-table is already defined. The only way to apply the customization is to somehow re-evaluate the variable (e.g. go to source code and C-M-x on it) which is 1) annoying, 2) requires you know Elisp at least to some extent. Worse yet, if you (require 'python-mode) above customization stuff (yes, as suggested in INSTALL), customization won't take effect even if you restart Emacs.
Customizations should take effect immediately or at least after I C-x r a buffer.