In Elizabethan times, plays required a license from the Master of the Revels, who would censor anything illegal (references to rebellion or religion for example

In Elizabethan times, plays required a license from the Master of the Revels, who would censor anything illegal (references to rebellion or religion for example). Google should supply plenty of details. Generally, though, the monarchy of the time was quite supportive of the theatre. Just as well really, as the City of London was run by Puritans at the time and they'd gladly have shut down every one of the theatres. That's the reason they were generally built outside the City.