Perhaps these people of whom you speak have found that “Christian” is the best qualifier to describe them…better than others. It distinguishes them, in a way, from Catholic and Orthodox (though all of us are, in fact, also Christians).
Perhaps they don’t use the qualifier “Protestant” because that is not at all how they see or understand themselves…or their origin. In history, the word actually does have a specific meaning and specific application. Not every follower of Jesus Christ in the West who is not Catholic is for being non-Catholic, thereby, “Protestant.”
In my years with the ecumenical dialogue, I have known and interacted with many who not only did not identify themselves in terms of the events of the 16th century, they did not identify themselves with movements within Christianity of the immediate subsequent centuries either.
Imposing a title on others that is neither historically accurate nor of significance or meaning to the ones being identified is rather non-serving both to them and to us.
It is rather off-putting when people use in my regard qualifiers which do not do justice to my self-understanding of my own identity.
Rather the Council Fathers of Vatican II, in Unitatis Redintegratio, gave guidance in how to proceed:
The term “ecumenical movement” indicates the initiatives and activities planned and undertaken, according to the various needs of the Church and as opportunities offer, to promote Christian unity. These are: first, every effort to avoid expressions, judgments and actions which do not represent the condition of our separated brethren with truth and fairness and so make mutual relations with them more difficult; then, “dialogue” between competent experts from different Churches and Communities. At these meetings, which are organized in a religious spirit, each explains the teaching of his Communion in greater depth and brings out clearly its distinctive features. In such dialogue, everyone gains a truer knowledge and more just appreciation of the teaching and religious life of both Communions.
In a few short weeks now, we begin the joint commemoration with Lutherans around the world of the Reformation. I am reminded of an early passage in From Conflict to Communion, which is the underlying document to the joint commemoration
10. In the last century, Christianity has become increasingly global. There are today Christians of various confessions throughout the whole world; the number of Christians in the South is growing, while the number of Christians in the North is shrinking. The churches of the South are continually assuming a greater importance within worldwide Christianity. These churches do not easily see the confessional conflicts of the sixteenth century as their own conflicts, even if they are connected to the churches of Europe and North America through various Christian world communions and share with them a common doctrinal basis. With regard to the year 2017, it will be very important to take seriously the contributions, questions, and perspectives of these churches.
I would take this even farther. There are communities that have arisen within the last century for whom there is no interest in comparing, contrasting, or defining themselves in terms of Catholicism or Orthodoxy…or the communities which emerged relative to the thought or inspiration or struggle of Luther, Calvin or Zwingli.
I would not over-think the issue of having to explicitly say that, when you use the qualifier Christian, you do not thereby disqualify Catholics as being Christians. When I reference a priest who is of one of the Orthodox Churches, I do not thereby convey that I consider myself to be a heterodox priest! When I refer to myself as Catholic, I do not convey thereby that Orthodoxy is not, in fact, also universal in its extension.