I think that "BUT" is quite important. With that "BUT" the Nazies might not get into control. "You can participate in democratic election BUT you must stay a democracy". The same thing is with Muslims. "You can push to whatever agenda you want BUT it cannot take basic rights from another".
For the purpose of freedom of speech or whatever, the liberals are pushing exactly the opposite from that by allowing those who reject freedom of pretty much everything get into control. Liberal views make sense when everyone plays by the basic rules of democracy and not taking someone else's basic right.