Mostly, NPR isn't publicly funded. It gets about 1% of its funding from the federal government. Public radio stations that carry NPR shows get more, but it's only about 17% from federal, state, and local governments. Some of them are also funded by universities, some of which are public.

If donating to NPR is a tax write off, it is publicly funded. If the majority of those donors are politically biased, they will create a feedback loop where news is catered to those donating to them. This isn't wrong per se, but just what it is.