To the best of my knowledge, Ivo (the developer) hasn't coded any backdoors in Classic Shell.
You can check out the source yourself of the current stable version to check for yourself. The new beta version's source isn't open for reasons mentioned here:
http://www.classicshell.net/faq/#general_oss Disabling it in the firewall will only cause it to be unable to check for updates, no other functionality should be affected.
As for stability, except for a rare crash which any software can have due to some incompatibility with other software or rare software/hardware configuration, Classic Shell is extremely stable. On production servers, it is recommended of course that you download the stable version which is used by millions daily. For extra stability on the server, you can install only the components you need.
The Start Menu EXE hooks into the Explorer.exe process, so if ever Explorer crashes become a problem in a very rare event, you can simply open the menu with a shortcut to ClassicStartMenu.exe and the -nohook parameter pinned to the taskbar.
Although -nohook is really intended for troubleshooting, not for regular usage, do not use it. For regular usage, it's safe to run the Start Menu and allow it to hook into Explorer.exe (that is the only way it can integrate well with the system). It is extremely stable.