Just so that everyone’s clear…
According to Protestant theology, the visible church is composed of all who call themselves ‘Christian’ and profess the essential doctrines of the faith.
On the other hand, the invisible church is composed only of the elect. This is why Peter, instead of addressing his letter to the ‘Church’, addresses it instead to the ‘elect’ (1 Peter 1:1). This is also why Paul says that he endures all things for the sake of the ‘elect’ (2 Timothy 2:10). According to Protestant theology (and the Scriptures!), the non-elect within the visible church are interlopers.
As to the charge that this doctrine cannot be found in church history (as if the Bible isn’t part of church history!), I cite two of the fathers:
“For it is not now the place, but the assemblage of the elect, that I call the Church.” –Clement of Alexandria, The Stromata 7.5
“The second rule is about the twofold division of the body of the Lord; but this indeed is not a suitable name, for that is really no part of the body of Christ which will not be with Him in eternity. We ought, therefore, to say that the rule is about the true and the mixed body of the Lord, or the true and the counterfeit, or some such name; because, not to speak of eternity, hypocrites cannot even now be said to be in Him, although they seem to be in His Church.” – Augustine, On Christian Doctrine, 3.32