RewriteRule ^(.*)$ dispatch.fcgi [QSA,L] line in .htaccess ruins access to .css files.

Alright.. I've found that if I enable that line in the .htaccess file to use the fcgi, then it doesn't load the site with the stylesheets.
If I comment out that line, then it naturally impacts the speed, but at least the site looks right.

Is there a workaround for this?