Certainly Andrew Lambert and Jack Widden are more able to answer this point more fully than I, but I will add what I can. Corbett's attitude towards Mahan, at least professionally, appears to have been one of respect and appreciation.
Ralph, I am not sure what you mean by "cheerleader." If you mean what we now call navalists, the UK had them in abundance. And not just the unthinking kind (although there were not a few of those, Kaiser Wilhelm comes to mind).
Here are some: Sir John Jacky Fisher, Pollard, Prince Louis of Battenburg (later Mountbatten), Sir John Jellicoe, Admiral Ernle Chatfield, and on and on, one might even include Winston Churchill, although he was more a chauvinist on that score at the beginning but his understanding that sea power underwrote British greatness was very firm.
While I neither know nor care much about the relations between Messrs. Mahan and Corbett I can comment on the social aspects. The English gentry was a relatively flexible institution by the C19 and C20. In essence, if you had the manner and speech of the gentry (allowing for fairly wide regional variation) and could afford to keep the style of the gentleman then you could win wide acceptance of your claim to gentle status.
Thanks for alerting us to this kerfuffle within the Naval subculture. Two questions: did the Royal Navy have a more devoted cheerleader than Alfred Thayer Mahan? And might this not be simply a case of the Mother Country's reflexive snobbery toward us shabby Colonials?
June Handgrenade 2020
Nate, The grenade is out, but there is another issue. That is the issue of the influence on the American officer corps (army and navy) by Jomini through the mechanism of West Point instruction as delivered by Henry Halleck and Dennis Hart Mahan.
Carol Reardon's excellent book--With a Sword in One Hand and Jomini in the Other--, as well some older scholarship by Russ Weigley, provide a more complex answer to this question, and thus, by association any influence on A.T. Mahan via his father or the crucible of West Point where he spent many (but not all) of his adolescent years.