Stylebot has never collected and will never collect any personal data, browsing history etc. The permission to access websites is to only let you customize the CSS for any webpage and automatically apply your CSS when you visit the webpage in the future.
In the future, Stylebot may collect browser version, platform name, user's settings (except website list or any other data which can help identify user). This information is needed for decision on implementing new features, removing unused features or suggesting default settings for new users. It will happen only with your permission.