and not *arguably*, but THE largest single change Tolkien ever made, IMO!  And one that I still have problems with.

Not until the '30 Sil was it firmly established by JRRT that Beren was to be a Man.  But I don't think him being an Elf would alter much of the story.  Beren the Noldo was not considered superior in any way, in fact in the early conceptions, there were many lowbrow Gnomes/Noldor wandering ME, some of which were former thralls of Morgoth, and Thingol thought of them all as "treacherous, cruel & faithless".  Luthien even introduces Beren to Thingol as a "wanderer from beyond the Bitter Hills."  Thingol, of course, has no problem with feeling superior here, and denegrating the outsider that's in love with his daughter.  So, in either case, I think Beren is definitely 'marrying up'.

The single biggest problem I have with Beren being a Man, is his unheralded & unexplained appearance in the Halls of Mandos following his first death.  The Gift of Eru is sacrosanct to my reading of Tolkein, and the Valar have no business with Men's souls (Turin is only prophecy, and Tuor's true fate remains unknown).  The fact that Beren was originally an Elf in the Lost Tales, the most lengthy & detailed versions we have, and inconsistently stayed so for so long, is probably the reason his Mandos appearance never disappeared.  And the knowledge that JRRT eventually made Beren into a Man, primarily due to his preoccupation with seeing himself as Beren with respect to his own relationship, further erodes the argument for me.

Since I do try to find consistency in different versions, in order to enjoy them all (& logical explanations seem to present themselves amazingly well, usually due to scribal error or mythical nature), this has always been the toughest one to rationalize.  However, I do concede that he was a Man, but only for the following reasons, in increasing order of rationalization:

(1.) LOTR/Aragorn (but even here it could be chalked up to ancient myth)  
(2.) JRRT's *very* first written reference had Beren as a man, then crossed it out to be Elf (but even CT notes that this probably only meant a male Elf, as the word 'man' was used as such throughout the LT) 
(3.) The Lost Tale is orally told by Elvish children, rather than more reliable tale-tellers such as Rumil. They even comment that this is the story as they know it.
(4.) Finally, in this case, the faulty nature of the Sil can be used to *support* what's written. That is, the fates of Beren & Luthien, including his temporary surfacing in Mandos's Halls, may be merely speculation & myth, as presented in the Sil.

Anyway, that's my theory of Beren, Beren!

(& PS, aren't The Avengers the World's Greatest Heroes?)