Yes, they count. As has already been said by others, “furry” when used to refer to the community is not limited to “creatures having fur” but is used broadly to cover all sorts of creatures including those with scales, feathers, etc.

I’ve been a dragon in this fandom since about 1995 and I don’t think anyone has ever said I don’t belong in the furry scene because I am covered in scales instead of fur.

If you like to present as some kind of animal person, then you are a furry.

The furry fandom is more about liking anthropomorpism and general animalistic features like tails and snouts (tho one doesn’t have to have all of them) than fur specifically. Consider synths, for example, which are an accepted furry species despite not having fur, not even being animals or even biological creatures, and just kinda being shaped like some sort of anthro animal but not any species in particular. Birds definitely fit.