First I must point out: Shows like "Wait Wait..." are entertainment and never present themselves or any of their guests as news or analysis or anything of the like. They don't need to be objective about anything they comment on.
Secondly: The conservatives make it pretty easy to make fun of them. They can write up a funny joke about a liberal going basaltic because no one is paying attention to global warming or they can write up a funny joke about a conservative who wants to stone to death sinners. I am not a professional writer or comedian but it is easy to spot which one would be more "fertile material".
That said, I do think there is a legitimate complaint about funding going into a general fund and being distributed to shows they don't appreciate. One can be a conservative and really love the news coverage NPR does but hate that any part of the funding they hand over goes to "Wait Wait..." To solve that would require changing how funding works with NPR.