You have to remember that pretty much all new music that came out in the early and mid 60s was classified as 'pop', i.e., popular music. We've since divided popular music into a million different subgenres. If the Beatles came out today, they wouldn't most likely be classified in the same subcategory as the Stones and the Who. In the 60s, they were all pop. Other British Invasion groups like Gerry and the Pacemakers, Herman's Hermits, etc. were lumped in with Stones, Who, Animals, Kinks and, to our more modern ears, they have very little in common. I mean, some of the artists in the RnR HOF who came out in the 60s would certainly not be classified as RnR now - Mamas and the Papas (folk), Joni Mitchell (folk), Neil Diamond (pop rock), et al. There just weren't the subcategories back then. It was all 'pop' or 'rock' even though, to our ears, there is a lot of difference between Cher and the Stooges.
Change the name to Music (or Pop Music) HOF and it would be more accurate. Then, Willie Nelson, Cher and the Beatles could peacefully reside together.