read the bible

[Aiza]

Can the Catholic church give any evidence to back up the 'accepted' authorships of the Gospels, according to 'church tradition'?

I'm unsure what you mean. There is the pious tradition that Matthew Mark, Luke and John were written by....well, Matthew, Mark, Luke and John. This isn't something actually held as true by the Church, and actually if you get the NAB, which is in use by the USCCB, they say that other people probably wrote them. When I say "Tradition" I meant the Big-T sense of the word.

The origins of those pious traditions are as follows:

Matthew: Is from a very old semi-ambiguous statement from St. Papias of Hierapolis (and we can't even know what Matthew he is talking about, or if he is talking about just the sayings (Q) or the discources or what language). It also is the only Gospel which names Matthew, instead of just calling him Levi. Matthew uses Mark as a source though and it makes no sense that an Apostle needs to look at someone elses' Gospel. My Catholic Bible lists "unknown" for the author. I'll also add that it was probably a Jewish Christian.

Mark: Was written by St. John Mark according to St. Irenaeus (a Church Father, disciple of St. Polycarp). He was a disciple of St. Peter, and all the anecdotal passages contain St. Peter in some way. There's no real reason why this should be right or wrong, my Catholic Bible lists "A Gentile Christian, possible a disciple of Peter's named John Mark"

Luke: Is a 2 parter with Acts of the Apostles, which goes in-depth into St. Paul's ministry and shifts into first person at times. St. Luke was a follower of St. Paul, and many Church Fathers stated he was the author, our earliest manuscript also claims him as the author. Contrasting view is that the Gospel does differ with St. Paul in a few areas of theology and some aspects of St. Paul's life. My Catholic Bible lists "a Gentile Christian named Luke, who may have been a disciple of Paul's"

John: Identifies its own author with the "disciple who Jesus loved", which of course in Christian tradition is St. John. It doesn't seem to be an eyewitness account though and it uses the plural "we know that his testimony is true", though its theology is Johannine. My Catholic Bible lists "a member of a Christian community possibly founded by the Beloved Disciple". There's also it was written in layers by said Johannine community, also most likely Jewish though a Jewish Christian who had already broken away from any Jewish community.

There are significant numbers of Catholic clergy nowadays who would reject Moses actually wrote the Torah or that Matthew, Mark, Luke and John wrote the Gospels.

Um, not just "significant numbers" but those are all probably majority opinions in Biblical scholarship. My Catholic Bible lists "unknown author who gathered oral traditions from tribal epoples sometime from 1225-1000 BC" as the author for Genesis, "unknown author gathering oral traditions and stories from various tribal peoples" as the author for Exodus, "Priestly writer writing after Babylonian exile"as the author of Leviticus, "priestly scribes writing during the Babylonian Exile" as the author of Numbers, and "scribes from the eighth century BC adapting the earlier Covenant Law to Israel's changing situation" as the author of Deuteronomy.

I would have to disagree, if it these were their own books then they would be independent works yet it seems that there is a lot of interdependence in the books of the bible. Therefore, coupled with the fact that it is a collection of books in one publication (which is also a type of book; Anthlogy), I would claim that it is one book written by many authors, like a really dysfunctional game of consequences.
Books should certainly not be read

in light of Tradition and Magisterium

as this is unquestioning and nobody ever changes anything by accepting it unquestioningly

They are mainly independent works, with a few exceptions (and even then they can be read independently). They were written from the same deposit of Tradition but weren't written with any 'interdependence' as you say. And they were kept as separate books until [relatively] recently. Orthodox Christians still usually keep them as separate books.

Tradition and Magisterium are that which illuminate Scripture. Without these, Scripture is dead text. If, as a non-Christian, you want to "question" these things, you can. Reading the fullness of Christian beliefs does make it more difficult to "question", but your "questions" are more well-informed I think. Picking out disembodied pieces of random scriptures is very easy, but your questions are almost always quite inane and not applicable to Christianity.

Hell, with the Magisterium, you don't need to read the fucking thing at all. They'll do that for you AND tell you what it means.

Well...technically this is true. You don't "need" to read the Bible to be a good Christian, though you should if you are able. The writing of most of the NT and the compilation of those particular books into a single collection known as "Sacred Scripture" was done by the Magisterium. It seems very weird to me to take one without the other, and pretend that "the Bible" simply fell out of the sky one day fully formed.