Do Paul and Jesus disagree on homosexuality? Romans 1:26-27:


  [26] For this reason God gave them over to dishonorable passions. For their women exchanged the natural sexual relations for unnatural ones, [27] and likewise the men also abandoned natural relations with women and were inflamed in their passions for one another. Men committed shameless acts with men and received in themselves the due penalty for their error.


Jesus said nothing about homosexuality (from what we know) yet Paul teaches strongly against it (continuing in other verses). How do Christians who believe homosexuality is wrong justify the potential discrepancy here?
You are correct in stating that there are no recorded teachings of Jesus on homosexuality.  However, to suggest that this means there is disagreement between Paul and Jesus is unreasonable, since it is comparing something to nothing. It is certainly wrong to assume that Jesus disagreed with Paul on that just because He never explicitly indicates His agreement -- with Paul and the Law of Moses.  

Indeed, if Jesus had disagreed with Moses on this, we should expect to hear about it in His teaching. If, however, He agreed with Moses, then why go to great pains to point that out?

It should be noted that Jesus was Jewish and lived among Jewish people in a Jewish culture.  This whole culture was based on Mosaic teachings that held that homosexuality was wrong and had a very stiff penalty spelled out for it, much like adultery. People caught in adultery still suffered the possibility of death (see John 8:1-11). It is quite likely that this was simply not practiced in this culture.  

Jesus never taught that eating pork was wrong either, because everyone in that culture agreed with that and no one ate pork. The idea of "preaching to the choir" about getting involved in the church comes to mind.  

During Jesus' life, Israel was still under the Old Covenant, so the prohibition against eating pork was still in effect. Paul's writings occur in the New Testament, but reaffirm the prohibition of Moses against homosexuality.

So, there's absolutely no "discrepancy", and any intimation that Jesus supported homosexuality is not reasonable.  

Jesus "did not come to abolish the Law, but to fulfill it" [Matthew 5:17].