If only a fraction of their budget comes from taxpayers, then why all the whining?
If I took money away from you, any amount, after you'd already budgeted for it, would you not complain?
I'm going to try -- hopefully not in vain -- to expand on BigA's answer in way that will dismiss the original question. (Everyone who hates me already, get ready to click on "Report" because I'm being mean.)
Let's pretend that Zebra has a brick-and-mortar retail business of some sort. Now, let's say that one of his long-time customers, who has always paid their bills in a timely manner and in full, needs something that has to be special ordered, non-returnable. Zebra will go ahead and order it with payment on delivery to the customer, because he knows the customer is good for it.
The item comes, Zebra pays for it himself ... and then the customer comes in and says "sorry, but now I don't have the money to pay for it, because something unanticipated happened." Zebra now has a big gaping hole in his budget because he spent money that now isn't coming from where the budget expected.
That is what is happening here. For many years, CPB was that customer and the public broadcasters were the business owners. They were told by the good customer how much they were going to "spend" with the "business" based on a reasonable expectation of their own financial "income" (the annual appropriation). So the stations created their budget knowing that they were going to get that money from CPB. Then that good customer suddenly isn't going to have that income, through no fault of their own, and the stations have a gap in their budget.
Just as my pretend scenario creates the probability that Zebra would ultimately have to close up shop because he couldn't make up the deficit from normal sales, public radio is in clear danger of having to go silent because they can't make up the deficit from normal fundraising operations.
▼ The "report" link is down here under my signature.