One way to view NPR as state-sponsored propaganda is by looking at the connection between NPR and the Open Society Institute, an organization representing the deep state run by George Soros.
It is exceedingly unlikely that a 1.8 million dollar donation will be given for nothing in return.
"(...) the Open Society Institute opted against on-air credit for its $1.8-million donation to NPR last year"
First: do we acknowledge the existence of a deep state? The existence of a deep state is troubling because a deep state can be more powerful than the official state which is in our case elected. A deep state can undermine and destroy the official state. It seems that the argument put forth by the GP is that NPR is a mouthpiece of the deep state, and not the official state.
My feeling with discussion about the "deep state" is that it understates the difficulty of organization. It's hard enough to get an explicitly public/structurally aligned/highly incentivized group of workers at a company to stay organized (the failure of the unionization movement is a stark example, but even mainstream companies struggle).
More likely, it is that careerists naturally produce work that reinforces long held beliefs and values - it's a big ship and it doesn't turn quickly. If leadership comes in and starts doing things that work against those values then the careerists might fight those directions, do them slowly, do them poorly. In a small company those underperforming workers would probably be fired. In a very large enterprise it might be difficult to locate those workers and/or costly to replacement if they have specialized knowledge/skills.
How is NPR state-sponsored propaganda? They've been some of Trump's harshest critics IMO, even after he became POTUS.