The Church via the Councils of Trent, Vatican I and Vatican II simply set out the Catholic Faith for both Catholics and Protestants to accept or reject. Those who accept the dogmas and doctrines set forth in these Councils and the magisterial teaching they engendered are Catholics. Those who do not accept them and vociferously oppose them or 'protest' against them are Protestants.
Now there are many who claim to be Catholic yet 'protest'  vociferously against the teaching of the Catholic Church; how are they to be regarded? Protestants is the word which springs to mind.
"Those who are not with me are against me", saith the  Lord.