"Ethical fellowship" is a sort of a keyphrase for secular beliefs that there are right and wrong actions distinct from any religious framework, as per Felix Adler's Ethical Movement. So Father Brown is basically alluding to two secular (often associated with atheism) movements, evolution and ethical fellowship, to take a dig at people believing that anything spiritual is merely hypothetical or metaphorical.
As per "Basis and Obligations of Ethical Fellowship" (bolding mine):
The Ethical Movement is based on the belief that the good life is the supreme object of human endeavor, and that mutual help and combined effort are needed to attain that object.
Its bond of fellowship is the desire -- nay the imperious sense of man's sacred duty -- to realize this goodlife; to be continually confirmed and aided in practical devotion to it; and to see more clearly and widely wherein such a life, in all its personal and social requirements, consists.
The significance of such a bond may be appreciated by comparing it with that which ordinarily binds men in sectarian religious association. The latter involves an agreement to think alike upon certain disputable problems as to the ultimate meaning of human life and man's relation to the world in which he lives. On the other hand, this bond of ethical fellowship is based on the common recognition and pursuit of a duty, binding upon us all, of living according to conscience and knowledge....
Amusingly, the choice of "ethical fellowship" may have resulted from a personal grudge as per an account in Ian Kerr's G.K. Chesterton: a Biography:
.... The 'immeasurable annoyance' with which Chesterton had to decline an invitation to 'sup' with the publisher John Lane and his wife was 'increased by a bitterly ironic fact' that he was 'engaged ... to lecture to a body bearing the wonderful name of THE PECKHAM ETHICAL FELLOWSHIP. Isn't it too beautiful? I'm sure they come out of a book. I only wish they'd go back into it.'