Erik,
XenForo 1.0.2 uses the following <html> tag:
<html id="XenForo" lang="{$visitorLanguage.language_code}" class="Public {xen:if {$visitor.user_id}, 'LoggedIn', 'LoggedOut'} {xen:if {$sidebar}, 'Sidebar', 'NoSidebar'}" xmlns:fb="
http://www.facebook.com/2008/fbml">
You should therefore be able to apply specific styling using html.Sidebar ... and html.NoSidebar as the first element in your CSS selector.
K