If you're okay with cherry picking then what does it matter what others think?
This is probably a false dichotomy unless you define cherry picking to mean ignoring what others think. It's possible to be very engaged with what others think but still to arrive at a slightly different perspective. Part of the problem is this ambiguity about the phrase. As a Christian, I think it would be a dubious enterprise (both spiritually and intellectually) to attempt to interpret and understand the New Testament in isolation from the ~2k years of tradition surrounding its interpretation, or without engaging at all with expert opinions on things like textual criticism, ancient history, languages, and etc. This isn't particularly surprising though. The analogous statement would be true in almost any field, from an intellectual standpoint.
if one thing is wrong then why not all of it? If one thing is corrupted then why not all the things?
I think the question presupposes a criterion for establishing the value of religious tradition which is untenable, and one which you wouldn't apply in other areas. We don't reject entire political traditions out of disagreement for some subset of ideas, or reject a mathematical approach to physics because old theories need correction.
I think fundamentally the problem with this attitude is it neglects that religion is a human enterprise, and as such is bounded by human limitations. That's why you note that it's "a matter of interpretation". That matter is inherent to the process. Even accepting some text to be a revelation from God, it still finds its way to us having been sifted through the beliefs, interpretations, understandings, and worldviews of the people who received it. There's a principle from scholastic theology, I think from Thomas Aquinas: "whatever is received is received according to the modality of the receiver". Which is just a technical way of saying that our understanding is always conditioned by our humanness. This idea is why, both in Catholicism and in Eastern Orthodoxy you may hear it said that it is the authors, and not the text in itself, which are inspired by God.
If we understand a religion to be defined by a set of dogmas, then the process of interpretation has to grind to a halt somewhere, at which point the "religion" came to exist. In this case, cherry picking is always "heresy". This would be historically problematic though, because in fact at no point has any major religion just suddenly appeared with an exact and fixed set of beliefs. The decision of which set defines the religion is entirely arbitrary, when in fact, the authors of the canonical texts themselves were engaged in the very process of interpretation that would be excluded. Paul's reinterpretation of Old Testament prophecy and the purpose of the Law, in light of his belief in the death and resurrection of Christ, is a perfect example of that.
If we understand a religion to be defined more by the common life of some group of people, not rigidly and dogmatically defined, then this issue goes away. It also turns out that this other kind of definition makes much more sense of the history of religions than the former.
