Hmmm… I must admit I don’t understand why Catholics teach that their church is always infallible. I can understand teaching that its TRUE, but I just can’t comprehend a belief that it was always true, on every minor and major doctrinal point, throughout all history. It would seem improbable, even for a church guided by the Holy Spirit, for even Godly men are fallible, and liable to err in one way or another. Most of the churches I know believe they are correct, but embrace at least the hypothetical possibility that they could be wrong about, say, their interpretation of Genesis and that if the Holy Spirit corrects them, they will change their doctrine. So possibly my viewpoint won’t be of help to you, but I will give it anyway.
I think there are two questions here, really:
One is “can it be fallible and still always be in alignment with a hypothetical ‘True Church’ that has no doctrinal error at all”? The other is “can it be infallible and still Christian, that is, in a state of grace, salvation, and unity with God”?
In the first case, the answers you have thus received are obviously correct. You cannot be both fallible and always true, just as you cannot be false and infallible. The one precludes the other. A church that is wrong in one doctrinal point is fallible and thus not in alignment with the actual truth on the matter.
That being said, your real question seems to be about whether it can be the “true church.” If I understand correctly, what you meant when you said “true church” was something like what C. S. Lewis meant when he referred to “the Church…spread out through all time and space and rooted in eternity, terrible as an army with banners.” That is, you appear to be wondering whether it is still the Church Christ calls His own – the True Church, not those temporal and spacial constructs we spend our time praying and worshiping in, but the true, timeless Bride itself, the sum of all those who are truly “in Christ”. Am I correct in this assessment?
Then, your question seems to become – supposing a) that this particular church is fallible on some point, and b) that we look at the Christians who are in unity with this church, would these believers, who are in unity with this fallible church, really be in unity with God? That depends on the doctrinal error, obviously. An error about God and Jesus and salvation is of a higher nature, an error about baptism and so forth of a lower nature, an error about what is sin somewhat lower, and error about some interpretation of what prophecy means lower still, etc. (I give these only as very rough examples.) Those of the higher error are deadly or dangerous, those of the medium pressing, but unlikely to kill, and those of the least of minor of little consequence.
I think it probable that God does not expect his followers to be infallible on all points of teaching, such as what exactly happens when we baptize, or what exactly he meant we should do in this particular situation, or whether or not a particular act is sinful, so long as they put their faith and trust in him and follow his commandments. No one is perfect, neither in good deed nor in knowledge of what it truly means to be good. Thus, I hold that one can be in union with a potentially fallible church, but still part of the “True Church” of the saved, so long as the error is not a deadly one that prevents them from coming to a true understanding of God. [Interestingly, if I am not mistaken, this is also the teaching of the Catholic church, correct?]
Thus, even if the Catholic church is wrong on some matter (which you haven’t actually argued), assuming that they make no deadly error in doctrine, any Christian truly aligned with their teaching (and hence, with God) is part of the True Church.
Does this answer your question?
P.S. Looking back at your definition of Infallible, I see that you said it means “protection from error.” I’m assuming that you meant absolute protection, such that no error can be made, rather than protection from serious error, or merely guidance that keeps the church from straying too far from the True path.