The good news is that you can still access it on your smartphone, or by accessing the mobile site directly. You can also temporarily by disabling Javascript in your browser when visiting the site (specifically blocking scripts from bits.wikimedia.org). Using Firefox + NoScript is an easy way to do this.
The Wikimedia foundation have a technical description of how the blackout is implemented here.
Added: the stylesheet itself appears to be at http://bits.wikimedia.org/en.wikipedia.org/load.php?debug=false&lang=en&modules=site&only=styles&skin=vector&* so blocking that temporarily might help.
If you are managing a large number of users who need access, you can block access to bits.wikimedia.org/en.wikipedia.org/ which will allow access to content but screws up the layout.
