Most mainline Protestants view themselves as Catholics, and repeat the Apostles Creed which includes that.
However, Catholic and Roman Catholic are not identifical. To serious students of history, early Christianity was not monolithic. The churches in the East did not acknowledge the authority of the Bishop of Rome over the entire church.
The argument often is made that the Bishop of Rome began to claim universal authority because that city was the center of the Roman Empire. There also is the argument that the Pope replaced - essentially - the Emperor and many of the traditions continued. For example, the adulation of the Pope. Or, how the Pope has been carried aloft by the Swiss papal guards while the crowds shout 'Viva la Papa!' - the chant shouted 2000 years ago by the pagan Romans as their emperor was carried aloft by special guards. Etc.
What Christians should do it respect other Christians and work toward unity. Such unity would still permit differences but emphasize our oneness in Christ. In many communities, such as mine, there has developed a warm feeling between Catholics and most Protestants, and they worship and work together at times. This must make Christ very happy. It's silly to let different opinions on doctrine and such serve to divide us in the world today. No church has all the truth (sorry if that sounds like heresy). God is too big to be contained in any one creed or theology.
Happy Thanksgiving. We had a superb ecumenical Thanksgiving service last night. Only a few fervent evangelicals and a couple of priests missed it.