I would like to see the explanation of how they are Protestant since that is a sect of Christianity.
Prostestants still have many traditions that the Catholic Church (which is Christian) has. So I still need to see an explanation on how a non-denominational Christian is Protestant. Especially if there practices are more closer to Catholic Mass than Protestant. Or if they lean heavier to Anglican. Or one of the Orthodox Churches.
You seem to want to lump all Non-Catholics in the Protestant category, but would you include Russian Orthodox? or Greek Orthodox? Certainly not, but these are also Non-Catholic. Protestant is a specific thing rising from a specific time during the reformation. Protestants include Lutherans, Calvinists, and others, but the sects which came after do not fall into this category.
When people say they are "non-denominational", I think what they are saying is that they are getting away from dogmatism and doctrinal differentiation, and returning strictly to what the Bible says.
I think that their attitude is that if it is in the Scriptures, then they believe it. Some denominations deny this doctrine or that teaching, etc. I think that another term they use is "full gospel". People from all denominations who discover that the Bible has so much more depth, leave their own denomination, so they call themselves "non-denominational" as they join with others who have left their particular denominations for the say reason.
For instance, in the church I attend, there are people from every background: Catholic, Methodist, Baptist, etc. (But we don't call our selves "non-denomination". The church I attend is called "Assembly of God", and the 16 fundamental beliefs of the church are all backed by Scripture, from salvation to healing, and everything in between.)
one of the pandora box of the Luther's sola scriptura - every one could come up your own interpretation and set up your own church w/c up to now there are about 40,000 protestants denomination of chaos in theology, divisiveness and off course, competing sermons.... LOL