Don't have to be that old to appreciate the Stones. Now, sneaking them into IFB colleges back in the 70s... that's old.
My appreciation of them came about in the last 10-15 years. As a teen, I was into pop and disco; I began to listen to "classic rock" while I was in the Navy despite hanging with the PCC crowd. As I got older, my tastes turned towards the Blues thanks in large part to SRV. By the mid 2010s, I was listening to BB King's Bluesville regularly and learned how much of what I liked was so closely tied to the old blues masters like Muddy Waters, BB, Albert and Freddie King, Howlin' Wolf, etc... I began to appreciate Led Zeppelin, the Peter Green incarnation of Fleetwood Mac and yes, the Rolling Stones.