There is an important distinction we need to make. A man is saved (justified) by faith in Christ alone for salvation. A man who trusts in his own works will be lost. This is the teaching of the Scriptures, made especially clear in Paul's epistles.
That said, man is justified by faith alone in Christ alone. That is to say, man is not justified by having a correct understanding regarding justification. Thus, we do not exclude from salvation every person who has (in some way or other) a faulty understanding of justification, provided that he sincerely believes on Christ alone for salvation.
In consequence of the above distinction, we do not exclude people based on their membership in an apostate church or cult. A believer ought to experience growth that will lead them out of that apostate church, but there are many seducing spirits in this world:
Mark 13:22 For false Christs and false prophets shall rise, and shall shew signs and wonders, to seduce, if it were possible, even the elect.
Some churches teach a false gospel: the Roman Catholic (so-called) Church is one of these. That false gospel will not save. But (thanks in large part to the Reformers) there are now Bibles available to members of that church. They can read and find the same conviction that stirred Martin Luther. It's even the case, these days, that many priests of Rome teach a Protestantized message. Perhaps, in some such parishes there may be priests who are contradicting their church's teachings to be faithful to the Scripture. If so, whether on an individual level or on an institutional level, praise be to God!
Another church that teaches a false gospel is the Mormon Church. Its gospel also will not save. But there are Bibles in the hands of most Mormons, and they too can read these and be convicted by the Word of God. I don't know enough of Mormon culture to say whether the gospel may be preached in some wards by the leadership there. If so, again, praise be to God!
Nevertheless, those who do follow the gospel of Christ ought to come out of these churches. That too is the teaching of Scriptures. For it has been prophesied that there will be false teachers:
2 Peter 2:1-3
But there were false prophets also among the people, even as there shall be false teachers among you, who privily shall bring in damnable heresies, even denying the Lord that bought them, and bring upon themselves swift destruction. And many shall follow their pernicious ways; by reason of whom the way of truth shall be evil spoken of. And through covetousness shall they with feigned words make merchandise of you: whose judgment now of a long time lingereth not, and their damnation slumbereth not.
These days the idea of "damnable heresies" is not politically correct. "Heresies" itself is a bit strong for the typical person. But the fact is that these men will and have come and called themselves a part of us, though they are not in heart. What then is the Apostle Peter's exhortation:
2 Peter 3:17-18
Ye therefore, beloved, seeing ye know these things before, beware lest ye also, being led away with the error of the wicked, fall from your own stedfastness. But grow in grace, and in the knowledge of our Lord and Saviour Jesus Christ. To him be glory both now and for ever. Amen.
Beware of false teachers, dear reader, and whether you believe your current church is right or wrong in general, trust alone in Christ for salvation, as it is written:
Trust in the LORD with all thine heart; and lean not unto thine own understanding. In all thy ways acknowledge him, and he shall direct thy paths. Be not wise in thine own eyes: fear the LORD, and depart from evil.
P.S. By the way - to those who do already acknowledge truth of Sola Fide: just so you know, that itself won't save you. You're not justified because you believe in Sola Fide, you're justified (if you are) only on the basis of faith, and that being faith in Christ alone for salvation. If you think good theology saves - you're wrong. Theology does matter: but having great theology won't keep you from being in the category of those who on the last day, with many sincere folks with worse theology than yours, saying "Lord, Lord" etc.