Everyone should just ignore this heretic, who goes around deposing Popes based upon his own extraordinary intellect ...
Of course, he never bothered to look at the Latin of the time Leo XIII used what has been translated as "separated brethren" (I'm sure rather deliberately by the Modernists, possibly even the Americanists he had been at odds with).
But this intellectual giant here, who may possibly be able to decline a simple first declension noun, if he were looking for truth, would see that the Latin is ...
fratres dissidentes... which better translates to dissidents, as it's an active departure, using a verbal (gerund) form with an active voice, where the activity was the result of their volition ... and not a term like "separated", which is more passive and could be something entirely unintentional -- so like the difference between a child who got separated from his parents (say, in a crowd) vs. a child who rebelled form his parents and broke away from them (which is more the term "dissidentes", very similar to the English word we have that derives from it).
As for the term "brothers", as already been explained, we can be "brothers" in a natural sense, since we have the same Father, the same Creator, and this does not mean that they are fellow "Christians" in the theological sense (vs. the natural sense in which these groups might be called Christians ... as opposed to something else, like Muslims or Jews), or somehow still members of the Church, as this heretic here would slander the Pope as teaching.
In fact, Pope Leo quite emphatically teaches the EXACT OPPOSITE, spending nearly the entirety of Satis Cognitum on the subject:
Satis Cognitum:
Quote "There is one God, and one Christ; and His Church is one and the faith is one; and one the people, joined together in the solid unity of the body in the bond of concord. This unity cannot be broken, nor the one body divided by the separation of its constituent parts" (S. Cyprianus, De Cath. Eccl. Unitate, n. 23).
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"Whosoever is separated from the Church is united to an adulteress. He has cut himself off from the promises of the Church, and he who leaves the Church of Christ cannot arrive at the rewards of Christ....He who observes not this unity observes not the law of God, holds not the faith of the Father and the Son, clings not to life and salvation" (S. Cyprianus, De Cath. Eccl. Unitate, n. 6).
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The practice of the Church has always been the same, as is shown by the unanimous teaching of the Fathers, who were wont to hold as outside Catholic communion, and alien to the Church, whoever would recede in the least degree from any point of doctrine proposed by her authoritative Magisterium. Epiphanius, Augustine, Theodoret, drew up a long list of the heresies of their times. St. Augustine notes that other heresies may spring up, to a single one of which, should any one give his assent, he is by the very fact cut off from Catholic unity. "No one who merely disbelieves in all (these heresies) can for that reason regard himself as a Catholic or call himself one. For there may be or may arise some other heresies, which are not set out in this work of ours, and, if any one holds to one single one of these he is not a Catholic" (S. Augustinus, De Haeresibus, n. 88).
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But he who dissents even in one point from divinely revealed truth absolutely rejects all faith, since he thereby refuses to honour God as the supreme truth and the formal motive of faith.
Contrary to the Vatican II teaching of a "Church of Christ" which is not co-extensive with the Catholic Church, Leo XIII teaches Traditional Catholic doctrine.
Now, one MIGHT use the term "brothers" or the term "Christian" in the natural sense, brothers being children of the same Father and Creater, according to nature, and "Christian" as referring to a natural classification rather than a theological one, but the actual ecclesiology of Pope Leo XIII that transcends semantics, especially as interpreted by someone who either is not able to or else is too lazy to actually look at the Latin, and then properly understand the meanings of terms.
At no point does Leo XIII state that heretics are somehow within the same Church as Catholics nor that they belong to the same body.