At least as it relates to whether a bishop is validly consecrated; teaching has little to nothing to do with it. Remember that ordination, in Catholicism, leaves an indelible mark that cannot be erased. Once a bishop always a bishop. A bishop who falls away from the faith in some manner is still a bishop. Any ordinations he performs would be illicit, but still valid. That’s why Rome has the concept of episcopii vagantes.
If that were not the case, Rome would not recognize the succession in the Orthodox, Old Catholic and Polish National Catholic Churches, which have “defied” the Church of Rome as well.
The reason, as I understand it, why Rome rejects Anglican succession is due to their modification to the rite of ordination of bishops, as well as intent, as well as the CoE now ordaining women.
When it comes to the Lutherans, many in Scandinavia are recognized by Rome as valid bishops, per what EvangelCatholic posted on the Porvoo Statement.