The issue is because Bing adds content before the <!DOCTYPE html> tag and the page is therefore prevented from being displayed as HTML 5.
When this happens, the browser stops distinguising between uppercase and lowercase in class names. XenForo has 2 classes: 'sidebar' and 'Sidebar' that are then assumed to be the same thing, which screws up the whole page.
As @Vincent says, this is probably a Service Issue because Bing/Yahoo should really not turn a HTML 5 page into a non-HTML 5 page. That being said, it could be fixed by not having multiple classes that differ only by their character case like 'sidebar' and 'Sidebar'. I would imagine it would be at least 1.3 before this would even be considered though.