At various times throughout the winter, I have seen either the male or the female Red-bellied Woodpecker at the bird feeder or on the trees near the feeder, but never together at the same time in the same place.
I have to admit that this shot is fake — I inserted the female into the photo of the male, just to test out another, different feature of Photoshop, and I haven’t quite got the knack of cutting and pasting an object into another photo yet.
But my purpose in showing them like this is to emphasize how similar in size they are, often not the case in many species where either the male or the female is substantially larger. Similar size and anatomy means that males would potentially compete with females for food resources in their breeding territory, unless they harvested it in different ways somehow.
If you watch closely, it does seem that the two sexes prefer to forage on different parts of the tree — the males more on the trunk and thicker branches, the females more on the higher, thinner branches. And, even though they are similar in body weight, males have a stouter bill and a longer tongue with a broader tip and barbed end, for harvesting insects deeper in the wood.