Prior to the 1960s lots of people used the term “Protestant” to refer to their Churches and themselves. Some local orphanages had the word “Protestant” right in their title. Nowadays you hardly find any person, church, or organization identifying itself as Protestant. The only ones who use that word seem to be Catholics when referring to those other Christians.
I wonder why that change happened. It’s unusual to find any trend that the most liberal mainline Christians, the most fundamentalist, and most moderate Christians seem to have in common. They all are called Protestant, and call themselves that, less than they used to be. In any event, my preference is to call people (as individuals) whatever they want to be called. If Anglican individuals want to be called Catholic, or Protestant, or some other term, as they express their personal faith, so be it, regardless of where they happen to worship or what they belong to.
I am not thrilled about every organization defining (or branding) their title however they want. If a congregation is in union with the Pope - such as the Ordinariate - the term Catholic is in order. I am not sure about Anglican organizations defining themselves (that is, the congregation, denomination, or other corporate entity) as Catholic, if they aren’t in union with the Pope. The factors that define a person are different from the factors that define a group.
I think at one time there were some kind of “standards” for (a church) being considered Protestant, at least in the USA. For instance, Methodists were “in”, Mormons were “out”. I think persons labelled Protestant have gotten so diffuse it is hard to rule anyone out now.
I know some would say there are many other criteria that define Catholicism - the sacraments, succession, Tradition, liturgy, devotion, etc - not just the Papacy. I can accept that, self-definition by individuals. But for organizations and churches, I would prefer rigid categories, not self-definition. I would hate to see the word “Catholic” used in so many ways that it becomes useless, like the word Protestant. C. S. Lewis described this process of losing valuable words by indiscriminate use, referring to gentleman, and Christian, as 2 examples.