I think that the Protestant churches are the ones that label themselves as ‘Protestant’ since it means they are protesting something the Catholic Church teaches.
For the baptism to be valid, it has to be done with flowing water (pour water on head, or submersion) and “in the name of the Father, the Son, and the Holy Spirit” to be valid. If this is left out or changed to their jobs instead of titles, ex: creator, redeemer and sanctifier, it is not valid.
Many main-stream ‘protestant’ churches meet this criteria. However, the ‘non-denominational’ churches vary so much from pastor to pastor, that no blanket rule can apply to them. One pastor may teach something extremely close to the true teachings of Christianity, and the next could be so far off that the only thing that links them to Christianity is the reference to the name of Jesus.
Now, I am not sure what you meant about being non-Catholic but not protestant… but I will expand on that to the point that I know. Typically to be understood to be Christian, they have to believe in the Holy Trinity. There are churches that believe that Jesus was just a man and not God, so they are out. And there are churches that believe in the Trinity, but they also believe there are other gods, so they are out (as far as being Christian).
Now, there are the schismatic Churches. Catholic means ‘Universal’ since they all follow the same doctrine rather than each individual church making up its own. In 1054 there was a dispute between the heads of the eastern Church and with Rome which caused the Catholic Church to be split into two Churches. Since, what is now called the Eastern Orthodox Catholic Church had valid Bishops and valid Priest, they have valid Sacraments to this day. In 1534 King Henry VIII split from the Roman Church and created the Church of England. Since his church was started with Catholic Bishops and Priests and for the most part, kept to the Catholic teachings, the Church of England’s Sacraments are also valid. These schismatic Churches could be called Catholic, though not ‘Roman’ (or Latin) Catholic since they deny the authority that Jesus gave Peter as the first Pope of the Church. Since these churches are ‘protesting’ the authority of Peter, they could be called both Protestant and Catholic.
This is why I identify myself as a ‘Roman Catholic’ rather than just saying ‘Catholic’.