: Are the Rohirrim Anglo-Saxons? I agree that they are not; they are an invention of Tolkien's. Were they influenced by Tolkien's knowledge of the Anglo-Saxons? I think they undoubtedly were.

: The bottom line is language, whatever the origin of Tolkien's use of a version of Anglo-Saxon for the speech of the Rohirrim (archaic English compared to modern = an archaic variant of Adunaic to Westron) on the page the words are Old English and this will unavoidably affect how the reader views the speakers.

: Other parallels between the two peoples are plentiful:

I do not think that the bottom line is language, rather it is how one choses to view the books. Do we pretend to take seriously the pretence that Tolkien translated the ancient Red Book and is revealing to us a lost era of our far past, and further, accept his rather unscholarly translation games, as explained in Appendix F, II? In that case, they plainly are not Anglo-Saxons, but a wholly alien people, and we may even regret the translation games and wish to know Theoden's "real" name and so on.

Or do we view them as part of a work of fiction. Then, plainly they are based largely on the Anglo-Saxons, a people Tolkien spent his life studying, who he loved and appreciated and regretted that they were fading from modern awareness. Taking that view, however, we should note that Tolkien is not so simplistic, that he has mixed elements drawn from many peoples of the northern world. The goths are most often mentioned as a secondary element. The Rohirrim are thus largely modeled on (an idealized, literary model of) the Anglo-saxons, they are not the Anglo-Saxons.

Or you can try to take a "stereoscopic" view, holding both points of view in mind at the same time, the richest way to approach this rich work of literature.