Not quite. All the groups listed only get a portion of their funding from the US Government, the highest amount listed was 15%. So the broadcasts would likely continue, just with fewer resources. The article also states that the funding is guaranteed by Congress, and the President can't impound it, but we've seen that Congress is letting the President break the law with impunity.
The article says that member stations rely the most on federal dollars. It would be ironic if cuts force member stations to close, and those stations happen to be predominately rural (and Republican). I bet Trump would use that as "evidence" of further bias ....
You get that news in like a tenth of what they do and if that's your issue just end the journalism and keep the shows because basically everyone loves them minus Nazis, bigots and morons.