“Let him be anathema” is just a formula to say that the preceding proposition is not the Gospel (it mimics the Apostle St. Paul who said if someone brings a different Gospel, let him be anathema). So when Trent says “if anyone says X, let him be anathema” it means that X is contrary to the Gospel. For someone to be anathema is to treat them as not a member of the Church–that’s where the “separated” in separated brethren comes from (others mentioned “anathema” as a canonical penalty, but this is something different).
The “brethren” part comes from that fact that all who are born again in baptism are the adopted sons of God. A bond is created through baptism that can never be broken, even by heresy or apostasy. That’s why we don’t re-baptize Protestants when they convert.
But remember, while heresy does separate from the Church, just being wrong does not make one guilty of heresy. As St. Augustine explained:
But though the doctrine which men hold be false and perverse, if they do not maintain it with passionate obstinacy, especially when they have not devised it by the rashness of their own presumption, but have accepted it from parents who had been misguided and had fallen into error, and if they are with anxiety seeking the truth, and are prepared to be set right when they have found it, such men are not to be counted heretics.
Someone born into a Protestant community nowadays is less likely to be guilty of the sin of heresy than someone at the time of Trent who made the active decision to defect from the faith.