Okay I will attempt to give an answer to this question that is based on evidence. It goes along the lines of the following websites:
My answer is that Protestants believe Paul's and Luke's writings for one main reason: they wound up in the New Testament Canon, and that the Holy Spirit wouldn't allow Jesus' message to be corrupted so the final Canon contains only 100% inspired and trustworthy writings, all heretical and apocryphal writings and having been eliminated from the Canon. Although this may be a circular reason, it has a logic to it -- after all, if the message has been corrupted, how do we know what to believe in the Bible?
In fact there seems to be quite a bit of evidence that would seem to make it very difficult to automatically place full trust in Paul and Luke. I will try to analyze the evidence step by step here.
First, Paul's own testimony should be scrutinized. For whether he is trustworthy or not, his own testimony should give us a basis to judge. Paul himself says that he didn't go to study with the actual students of Jesus after his conversion, but continued to receive visions and spread his message from his own understanding. After three years he went to see Peter, and wound up meeting with no one but James. Then fourteen years later he finally went, according to his own words, to meet with the "Pillars of the Church" - the one Jesus had established and gave authority to - and present them with his own gospel to the Gentiles he'd been spreading. As he tells it:
1Then after fourteen years, I went up again to Jerusalem, this time
with Barnabas. I took Titus along also. 2I went in response to a
revelation and, meeting privately with those esteemed as leaders, I
presented to them the gospel that I preach among the Gentiles. I
wanted to be sure I was not running and had not been running my race
in vain. 3Yet not even Titus, who was with me, was compelled to be
circumcised, even though he was a Greek. 4This matter arose because
some false believers had infiltrated our ranks to spy on the freedom
we have in Christ Jesus and to make us slaves. 5We did not give in to
them for a moment, so that the truth of the gospel might be preserved
6As for those who were held in high esteem—whatever they were makes no
difference to me; God does not show favoritism—they added nothing to
my message. 7On the contrary, they recognized that I had been
entrusted with the task of preaching the gospel to the uncircumcised,a
just as Peter had been to the circumcised.b 8For God, who was at work
in Peter as an apostle to the circumcised, was also at work in me as
an apostle to the Gentiles. 9James, Cephasc and John, those esteemed
as pillars, gave me and Barnabas the right hand of fellowship when
they recognized the grace given to me. They agreed that we should go
to the Gentiles, and they to the circumcised. 10All they asked was
that we should continue to remember the poor, the very thing I had
been eager to do all along.
Paul Opposes Cephas
11When Cephas came to Antioch, I opposed him to his face, because he
We aren't told the events from the point of view of Peter or James. We simply assume Peter must have realized Paul was right, and that they told Paul they approve of everything he's doing. To me, this is already a very strange conclusion -- simply taking Paul's word for it. What's even more strange is that it almost seems from what Paul writes that the Great Commission wasn't even given. https://www.biblegateway.com/passage/?search=Matthew%2028:16-20
Paul's writings quote the OT from the Septuagint, showing Paul was a Greek Jew from Tarsus (modern day Turkey). Many have remarked that Paul's writings don't show a great knowledge of Jesus' actual ministry and parables during his life.
This is a very serious question because without Paul's writings it's not obvious that Jesus taught not to follow the Law. It seems, in fact, that Jesus seems to have taught the opposite. First of all he said he came to the lost sheep of Israel:
He answered, "I was sent only to the lost sheep of Israel."
In the Sermon on the Mount, Jesus taught you shouldn't teach Jews to ignore the commandments given through Moses, something Paul explicitly did:
Therefore anyone who sets aside one of the least of these commands and
teaches others accordingly will be called least in the kingdom of
heaven, but whoever practices and teaches these commands will be
called great in the kingdom of heaven.
Rather than saying the Law was powerless to save, Jesus said this about the Ten Commandments:
In fact even as Jesus taught about the Son of Man being betrayed to the Gentiles, and will rise on the third day, he didn't say that the Law would be nailed to the cross.
This creates a high burden of proof that Paul and Luke are trustworthy, because if a Jew becomes a Christian he essentially has to take Paul's word for it that the law has been nailed to the cross. He has to place his faith in the words of Paul and meanwhile will have to bend over backwards to reconcile it with the explicit words of God in the Old Testament, which he has much better reasons to believe, as well as the words of Jesus:
Basing Paul's authority on his own epistles or the writings of his students is the same as Joseph Smith or Mohammad. Protestants are not Muslims or Mormons, so if they apply the same standard, that rules out this reason for accepting Paul.
The only place I know where leaders of the Jerusalem church are said to vouch for Paul is here: http://en.wikipedia.org/wiki/Second_Epistle_of_Peter ... but the problem is that most NT scholars don't believe it was written by Peter. As far as I know this removes the last piece of evidence that would give authority to Paul.
On the contrary, we see leaders of the Jerusalem Church following the Law long after the resurrection and even Pentecost, when they received the Holy Spirit and gained a lot of understanding. Furthermore, we know the historical Church in Jerusalem became marginalized over time, and the Ebionites, Nazarenes and Judaizers -- basically Jewish Christians -- were branded Heretics. Remember, though, Jesus said he was sent only to save the lost sheep of Israel. And he established a Church led by Peter and James. But something happened to them and the apostle to the Gentiles went on to found a bunch of Churches who then eclipsed the authority of the original Church.
The original religion of Jesus and his followers was called "The Way". And I see no way to rule out the possibility that Paul's ideas were, like Joseph Smith's and Mohammad's, basically innovations based on personal ideas and revelations. Paul was a Greek speaking Jew who always quoted from the Septuagint. Jesus' teachings focused on the Law and holiness, the Messiah and the Kingdom of God. Paul's ideas about Jesus being a blood sacrifice sound closer to the mystery cult religions of the Gentile nations at the time, which may explain why some people today like to make strained comparisons to the cult of Mithras or something similar. Jesus isn't clearly shown to teach anything like that.
So to sum up -- although I am not at all saying that Paul invented Christianity out of whole cloth, and not saying that Paul and Luke couldn't be saying the truth, I am aware of no solid reasons to automatically trust everything they wrote, and a lot of reasons that make it difficult for me to trust them when it comes to what God said and the teachings of Jesus, which stand on their own. My answer is that Protestants put faith in the way the Canon was compiled, and because of the way Christianity developed, Paul became quite a central figure to the early Church fathers and thus it is dogma today to put absolute faith in his writings. One might question, but that would be going against the official position.