And even if the browsers are identical there are still some ways to detect different user based on client side behavior (assuming JS is enabled, or some particularly crazy CSS)

Just giving the same value for everyone on the latest version of Firefox using Windows 10 with a maximized window on a 1920p display would seriously hamper fingerprinting. It can still be enough when used with other information (IP, visited sites etc), but at least it would dilute the signal a lot.

Section 3.2 'Advancing fingerprinting' shows some more ways you can find particularities which will be hard to hide.