Although XSLT 2.0 is not natively supported in Firefox, it is possible via Saxon-B (Java) or, more recently, Saxon-CE (JavaScript) to perform XSLT 2.0.
For users
Saxon-CE
No extensions are required, Saxon-CE runs whenever a HTML page is loaded that links to the Saxon-CE JavaScript library.
Saxon-B
The XSL Results extension uses the new incarnation of LiveConnect (handled by Java 1.6v12+ instead of Mozilla-specific code) to connect with the Java-based Saxon-B library, and adds support for having XSLT performed automatically when visiting a page with the appropriate XSLT processing instruction (and which isn't processed by Firefox's own XSLT 1.0 processor).
For developers
Saxon-CE
A JavaScript API is provided for initiating an XSLT 2.0 transform from a web page. Error and diagnostics output from Saxon-CE can be reviewed in the Firefox developer console or in Firebug.
Saxon-B
The extension demonstrates how one can use LiveConnect code to communicate with the Saxon-B library, but one might find the JavaScript code module approach used inside the extension XqUSEme as a more reusable approach.
The code does not currently work on the Mac (except for server edition supporting Java 1.6) due to its lagging Java support (and thus LiveConnect support).