All RES data (settings, user tags, some browsing history) is stored in your computer's browser. Data is not synced to a cloud service without you explicitly setting it up.
RES does not encrypt passwords stored in the Account Switcher. Would you like to know more, citizen?
RES stores some data about where you've visited recently on reddit.com. This data is also stored while using RES incognito.
RES requires access to certain functions of your browser and access to some external websites. Would you like to know more, citizen?
Reddit Enhancement Suite will check, at most once a day, to see if a new version is available. No data about you is sent to the RES team nor is it stored.
You can use RES to load stylesheets from outside reddit.com. None are loaded by default.
The websites hosting these external stylesheets can collect some data about you: your IP address, what browser you're using, and that you're loading the stylesheet from reddit.com. These websites can also add tracking cookies to your browser. These are generally safe, but if you are concerned about being tracked, do not add stylesheets from websites you don't trust.
RES has some features to help maintain privacy, but by and large RES is not a privacy/security extension.