The filioque denies the monarchy of the Father as the origin of everything, including existence itself. It changes the Church’s understanding, such as it is, of the very nature of God. To that extent it is heretical unless the 2 local Latin Councils which proclaimed it are in fact ecumenical councils, which Orthodoxy and so far as I know at least one Eastern Church in communion with Rome. hold. Many people understandably argue that it is too fine a theological point to stand in the way of a reunion, that the Laity simply doesn’t care or understand. Personally, I think that in the East that is demonstrably untrue and in the end it will be up to the Orthodox laity as to whether or not any reunion succeeds. You know, some Nestorians argued that the term Christotokos was as appropriate for Panagia as Theotokos, claiming the distinction between “Christ bearer” and “God bearer” was a distinction without a difference. We know what happened to the Nestorians.
I don’t believe that Rome is overly wedded to the filioque. In fact, the normative form for the Creed when being used for catechesis or when prayed in Greek is without the filioque. That said, I simply don’t see this being overcome short of a new Ecumenical Council.