Does Pope Eugene IV contradict Scripture?

Pope Eugene IV said that no one, even if he sheds blood for the name of Christ, can be saved, unless he has remained within the bosom and unity of the Church. Many people shed blood IN THE NAME OF CHRIST, but not for Christ.  The Protestants who reject the one true Catholic Faith and Christ's clear teaching on Confession (John 20:23), the Eucharist (John 6:54), the necessity of Baptism (John 3:5), etc. reject Christ’s truth, so their act of martyrdom is not for Him, but for Christ in name only– if it were truly for Him then they would accept His truth.  The same is true of the Orthodox Schismatics, who reject Christ’s clear teaching on the Papacy (Mt. 16:18-20) - so their act of martyrdom will profit them nothing.  The same is also true of all “Catholics” who obstinately adhere to heresy, but would pretend to shed their blood for Christ.  One example would be the “priests” and nuns of Mother Angelica’s EWTN.  They accept non-Christian, false religions as good and even “great” – and therefore reject Christ – yet some of them would probably go to death for the name of Christ if they had to.  Hence, they would still not be saved because they are not Catholic, unless they amend and accept the true Faith beforehand. So, Pope Eugene IV's statement does not contradict Scripture.