Celtic Pagans must be poets, even if they aren't great poets. Fourth, a connection with the past. The Celts had a reverence for history, and that reverence is a part of the Celtic spirit, I believe. For some, this connection comes through physical ancestry. For others, it comes through study of history.
Some people get it through connecting with the feeling of the myths.
Other folks get it in other ways. We all recognize that something from the past is speaking to us strongly, but we disagree about the methods of judging its veracity and usefulness. Much of this cosmology has had to be painstakingly reconstructed from fragmentary hints, and it goes back again to the argument that historical research is important to learning about and preserving the Celtic spirit. Sixth, I think that inclusiveness is important. We can't rely on genealogy or geography to determine who is Celtic.