Here's the passage:

But avoid foolish controversies, genealogies, dissensions, and quarrels about the law, for they are unprofitable and worthless.— Titus 3:9

Does this mean that we should never discuss interpretations of the law? Does this mean that differing interpretations of the law should never cause Christian brothers to separate from one another? I will show that both answers are "no." What does Paul mean, then?

Divisions in the early church

Paul was in a difficult position as an early church leader. Most of the early converts to Christianity were Jews. Their entire worldview was shaped by a group of Biblical laws which we'll call "Jew/Gentile separation laws." These included circumcision requirements, prohibitions on intermarriage, food laws, ritual "cleanness" laws, and some others. These laws had an important purpose in Israelite history, which was to prevent God's people from syncretizing (mixing culturally/religiously) with the surrounding Gentile nations. God made this purpose clear in the law; for example:

You shall not intermarry with [the Hittites, the Girgashites, the Amorites, the Canaanites, the Perizzites, the Hivites, and the Jebusites], giving your daughters to their sons or taking their daughters for your sons, for they would turn away your sons from following me, to serve other gods. — Deut. 7:3-4 ESV [underline added]

Pontius Pilate (Tissot)

The territory of Judea was not a good posting for Pontius Pilate: far from the seat of power in Rome, he was out of touch with the important developments in the Senate and Praetorian Guard. It was a volatile area, full of rebellious people. Vassal kings, various ethnic groups, and religious factions (like the Pharisees and Sadducees) were in constant friction with one another.

Now, during the Jewish Passover, Jews from all over the Empire were making their pilgrimage to Jerusalem to participate in the sacrifices. And Pilate had to go too, to show that Rome would not tolerate any outbursts of nationalism. Every so often, somebody would stand up, claiming to be an anointed king (messiah), eager to lead the people in a rebellion against Rome. So Pilate had to leave his nice residence in Caesarea — a modern, civilized, coastal community — and travel inland to that city which was the heart of his administrative problems.

Pilate (like most people in positions of power) had to be constantly on guard against being manipulated by one or another of the local interest groups.

Jesus before Pontius Pilate

Now, the Jewish chief priests had brought him another messiah pretender that they wanted executed: an unimpressive-looking man, with the common Jewish name Yeshua. Maybe Pilate could get a quick admission of guilt and be done with it.