While I think you're right in one sense- that most people when they think MiG21 v F4 it's with the Vietnam War in mind- I would argue that the -21bis, being that she entered service in 1972/3 is a natural contemporary enemy of the F-4E up until the late 70s when the Eagle et al where fully in service.
I say this with a hypothetical Euro war in mind but you could also extend it out to the various Israel/Arab states conflicts from the mid-70s through to maybe the early 90s I'd say.
All that said calling something a "rival" as if it was the only one is a bit of a simplification. After all, the MiG21bis was mostly used for point interceptions, specifically bombers as I understood it, the F4E for ground attack and Weasel, for the most part.