Your arguments seem to hinge on some hypothetical world where Republicans are in charge AND the executive agencies are all on board with their agenda. Then, to be "government funded" NPR would have to hew to the Republican line. Q.E.D.
Maybe the first part of that will happen someday. It hasn't yet. In fact, large parts of the civil service are permanently one party and do not change when the other party takes charge (as, indeed, the Civil Service reforms of the 19th Century set out to insure). Only about 4,000 jobs are politically appointed, according to Wikipedia.
If the executive agencies are imposing their agenda rather than the "government agenda", then, they are not biased for being "government funded", they are being biased for being "funded". If the government has no power, they could be "government funded", or "privately funded", or whatever, they are not manipulated by the government, they are manipulated by a lobby.
What you are saying is that there is a group of interest that are independent of the government, and that has an influence because they are giving money.
Why should we had a label when this group of interest is "the executive agencies", but not when it is "the investors of Wall Street", the "mass media conservative groups", the "christian lobby", ...?
(I don't pretend it's the case. I think people who really believe that the evil executive agencies impose their agenda are idiot who are not able to mentally comprehend that maybe NPR news are biased because their redaction is politically biased, with or without the existence of executive agencies)
(also, the reasoning on 4'000 jobs politically appointed is very weak: while there are way more than 4'000 jobs in the executive agencies, the very very very majority of these jobs have ZERO decision power, and the position of power in these agencies are the one politically appointed. If these executive agencies are sending memos to bias the media, or even renegotiating the contracts or the refunding based on what the media have published, it is with the support of the politically appointed board of directors)
Maybe the first part of that will happen someday. It hasn't yet. In fact, large parts of the civil service are permanently one party and do not change when the other party takes charge (as, indeed, the Civil Service reforms of the 19th Century set out to insure). Only about 4,000 jobs are politically appointed, according to Wikipedia.
So, no, you haven't gotten that out of the way.