There are some churches that are separated from the Roman Catholic Church on doctrine issues and some on organizational issues; there are Protestant churches that have formed from both sorts of schisms because they did not want to accept the RCC’s way of doing things, and the term is generally used to mean only those churches that broke away during the Early Modern Reformation. However, one could consider the question of whether these churches share the same characteristics as Protestant ones. Protestant churches affirmed themselves generally on justification through faith alone, the Bible being the source of all doctrine, and that all believers were capable of determining its meaning, not just the clergy. From this definition the Church of England wasn’t initially Protestant as the reason they went into schism is entirely organizational. After breaking with the Church politically they were more receptive to the ideals of the Reformation and so adopted many doctrines typical of them.
Recently, there are local churches that would like to continue to be part of the RCC, except that that the RCC has made some really stupid decisions in their eyes. For some urban areas, it’s closing down churches in the places where people actually go to church and leaving up the bishop’s church that no one attends any more. Thus, the congregation still wishes to be part of the church led by the Pope, but refuses to recognize the Pope’s delegated authority through their bishop. Thus while they want to believe that they are Roman Catholics still, and may feel in their heart of hearts that they are following the Church in all spiritual matters, but part of being in the RCC in reality is accepting the authority of the Pope and the Pope’s delegated officers in organizational matters as well. While their intent is pure, and they may accept the doctrine of the Pope, they are equivalent to the Eastern Catholic churches (not Eastern Orthodox, Eastern Catholic) that were in essence never organized from Rome but maintain spiritual deference to the Bishop of Rome’s doctrine. To call these churches Protestant is inaccurate, as there is no reason to believe that they will ever disavow the spiritual precedence of Rome.
If there’s priests out there who consider themselves part of the RCC still despite continuing to preach what has been ruled as heresy, they’re not good candidates for being called Protestant either as they still presumably hold most of the central beliefs. They have no desire to break from the church, but still refuse to recant their heresies. In this sense they are more like Arianism or Nestorianism, who disagree on some minor theological point that has little to do with how one approaches the religion, as opposed to Protestantism that goes an entirely new direction with what it means to be a Good Christian.