Safe Browsing is implemented in a fairly privacy-preserving way. The block list is downloaded periodically and sites are checked against this list locally. The only time most browsers implementing Safe Browsing will share potentially privacy-sensitive data is when you download executable files and when you actually encounter a site included in the block list (in order to double-check whether the site has since been removed).

Documentation for the Safe Browsing implementation in Firefox can be found here[1].

[1]: https://support.mozilla.org/en-US/kb/how-does-phishing-and-m...