The GQP isn't really going after PBS because of Big Bird
etc. They and their mega-donors and corporate overlords can't stand "Frontline", "American Experience", "PBS News Hour" etc. because those shows do investigative work into crooked actions by those folks. "American Experience" shines a light on history that they would like to erase and never have talked about again.
The fascists could care less about yoga programs in the morning followed by kids shows. They care about "Frontline" digging into corporate polluters, drug company scams, health care ripoffs and the lies and atrocities about things like the Iraq War. The big boys know that they own the major networks and so there won't be investigative documentaries there anytime soon and what little exists, like "60 Minutes", they're trying to kill any way they can. They know if they can chase programming like that out of the mainstream media and push it over to streaming outlets like Amazon, Netflix etc. then fewer and fewer people will see it and the fascists propaganda can take a better hold and do it faster.