Polar bears do actually eat birds. Seal is the staple of their diet, but being the most carnivorous of all bears they eat anything they can kill, including shellfish, rodents, beluga whales, walruses, musk oxen and on an extremely rare occasion… other polar bears.
Of course they don’t eat penguin since there are none in their location. I imagine penguin would be a pretty suitable food for them with the high fat content. But inexperienced polar bears would probably slaughter whole colonies of penguins or at least their chicks and be a threat to their population. I don’t think they would coexist in the same environment too well unless the Antarctic penguins learned to have more defensive nurseries. Perhaps burrowing in the ice like seals and some island penguins that burrow in dirt.