I feel like being a non Sede is kind of inherently an attempt to "have both" at a certain level.
"He's the Pope but I want nothing to do with him" only makes sense if you accept EO ecclesiology rather than RC ecclesiology.
Yes, that is the mindset behind sedevacantism and their criticism of R&R. It's much more than merely a debate about the strict limits of infallibility.
That is why there has always been this tension pulling on either side of R&R, with the FSSP and now neo-SSPX drawing back closer to the "Vicar of Christ," whereas the sedes realize this tension and pull away. It's currently the Resistance that is the last stronghold in maintaining both that Bergoglio is a legitimate pope AND that Catholics can, for all intents and purposes, want to have nothing to do with them.
Neither sedevacantists, nor FSSP, nor now the neo-SSPX believe that is a tenable position. If I believed with the certainty of faith that Bergoglio is the pope, I could find no fault with +Fellay's position, nor with that of the FSSP, nor even with the conservative Motu Catholics.