The RadControls of Telerik support any valid !Doctype
Additionally I have tested the proved markup, but the the described issue does not appears independent of !Doctype scenario.
Also I am not quite sure that I correctly understand what you are trying to achieve. The selector in CSS rule .RadFilter_Default.rfField have to be with interval between both classes, but it is still unexplainable why you need to render the anchers like block elements.
You can find my sample web site as attached file, check it out and let me know if missed something.
the Telerik team