You wrote: “Groups that seek to rewrite or create their own Bible are not Protestant.”
So where does that leave all of those self-admitted Protestant groups that cut the Deuterocanonicals from their new Bibles?
The Deuterocanonicals were NOT formally recognized until Trent, AFTER Luther sided with the scholarly school of thought which rejected their canonicity. Until Luther various loyal Roman Catholic scholars doubted whether they should be included in the canon. The very reason they are called “deuterocanonical” instead of just canonical is because even Rome recognizes their 2ndary authority to the rest of scripture.
Also, the word “catholic” has the definition of “universal.” All non-Roman Catholic churches consider themselves a part of Christ’s universal church, as do of course the Anglicans. So yes, as they understand the term universal, Anglicans are Catholic. Of course those submitted to the Bishop of Rome say they alone are The one and only universal church.
To the rest of us this seems so much arrogant nonsense.
I find generalizations detract from real discourse.