Given our modern culture, it should not be a surprise that I sometimes receive "shock" letters, for example questioning whether the Mary or even Jesus was alway a virgin. Below is a way of responding:
Concerning the argument that Jesus had sexual relations I have to admit from the start I cannot refute it. However, it is like the old "invisible cat" dilemna: If that chair had an invisible cat on it, that is exactly how it would look. Therefore that chair has an invisible cat on it. Who can disprove it?
However, to see if the argument really makes sense one would have to take a broader perspective. In the case of Jesus, it would involve taking a look at his overall historical context--as you indicate. But not only licentiousness (common to every age) but specific movements like the Essenes who valued celibacy and may have influenced Jesus--as well as Joseph and Mary. Most to the point of course would be the many New Testament statements from Jesus himself and his subsequent followers, re--the sanctity of marriage and call to life-long virginity and celibacy.
From a Catholic point of view, all this would show the need for what we call the "analogy of faith" (cf Catechism #114) by which individual parts of the Bible are interpreted in relation to the whole Scripture and the entire tradition of teaching in the Church. A good book on the is By What Authority? (Mark P. Shea). He shows how without the correcting role of Tradition almost any theory about Jesus can be justified. He mentions the current "Jesus Seminar" which argues that Jesus was an itinerate Stoic philosopher, that his body was not buried, but eaten by dogs, etc. This is nothing new. The devil himself used scripture verses when he tempted the Lord. Jesus knew well the need for an authoritative Magisterium.