How to disable a feature whose checkbox is grayed out?
This is true for Module page and Features page:

The page should list out the dependencies and modules/features that are dependent on that module/feature so you would have to turn off those modules/features before you can turn off the one that is disabled, if you use drush it will tell you that you are turning off all dependent modules when you perform drush dis modulename

One thing to note: on some setups that dependency list may be collapsed. Certain developer/helper modules will collapse those options on the modules page so you may have to click to expand but the reason why a module could not be disabled is b/c it is a dependency for another module so unless you are using drush like mentioned above you will need to turn off all the modules listed as needing that module to operate first.