When you tune into public radio you're most likely not listening to NPR. Public radio stations draw their programming from many sources, including in many cases shows produced by the station. NPR does distribute more content to public radio stations than do APM, PRI/PRX, or WNYC, but their programs don't comprise a majority of public radio content.
Unfortunately your litmus test especially doesn't work that well for NPR, at least in one example. They distribute (but do not produce - partly because it wouldn't meet their editorial guidelines) a show about issues facing Latin Americans in the United States called Latino USA. Yet nobody who listens to it would deny the show takes quite a strong progressive stance on political issues.
I'd also add that NPR's most popular shows, the newscasts Morning Edition, All Things Considered, and Weekend Edition, are all remarkably boring politically and take a sort of weaker sauce version of the BBC's neutral and somewhat hostile approach to interviewing, regardless of political bent.