Leto had been wise to choose this place for his seat of government. The name, Arrakeen, had a good sound, filled with tradition. (7.5)
Leto is indeed wise, or at least a very good politician. Have you noticed how every politician (ever) always gives speeches dedicated to tradition? It's because people love hearing how great their tradition is. Leto has done the same thing, albeit subtly. He promotes tradition simply by establishing his capital in a traditional-sounding city.
"The Harkonnens won't rest until they're dead or my Duke destroyed. The Baron cannot forget that Leto is a cousin of the royal blood—no matter what the distance—while the Harkonnen titles came out of the CHOAM pocketbook. But the poison in him, deep in his mind, is the knowledge that an Atreides had a Harkonnen banished for cowardice after the Battle of Corrin." (8.93)
The darker side of tradition and custom is that it can lead to conflict simply by trying to fulfill the demands of tradition and custom. Think this kind of stuff only happens in fiction? Heard of the Hatfields and McCoys?
"Before I do your bidding, manling," Mapes said, "I must cleanse the way between us. You've put a water burden on me that I'm not sure I care to support. But we Fremen pay our debts— […]" (9.44)
Cultures have can have many similar features while still being slightly different. In Fremen society, debts are thought of in terms of the water one owes. In Harkonnen society, it's all about the cash flow. What would you say is our society's version of the water burden?
"Sir, I honor and respect the personal dignity of any man who respects my dignity. I am indeed indebted to you. And I always pay my debts. If it is your custom that this knife remain sheathed here, then it is so ordered—by me. And if there is any other way we may honor the man who died in our service, you have but to name it." (12.145)
Leto honors the tradition and customs of another culture because it's the polite and respectful thing to do. Also, he probably doesn't want to kill anyone.
It was the custom, the housekeeper had explained, for guests as they entered to dip their hands ceremoniously into a basin, slop several cups of water onto the floor, dry their hands on a towel and fling the towel into the growing puddle at the door. After the dinner, beggars gathered outside to get the water squeezing from the towels.
"The custom stops here!" [Leto] muttered. (15.7-9)
Then again, sometimes traditions and customs just need to change. These two examples are pretty clear-cut, but in real life, the line between traditions that need altering and those that don't can get super tricky. Case in point: the way Americans argue over the Second Amendment.
Kynes shook his head, spoke in a lecturing tone: "Not the blood, sir. But all of a man's water, ultimately, belongs to his people—to his tribe. It's a necessity when you live near the Great Flat. All water's precious there, and the human body is composed of some seventy per cent water by weight. A dead man, surely, no longer requires that water." (16.147)
If you want to know what a culture values most, look at their funeral traditions and customs. The way a culture treats its dead will tell you everything you need to know about its values.
A tank-brain, the Baron thought. Muscle-minded tank-brain. [The Arrakis people] will be bloody pulp here when [Rabban's] through with them. Then, when I send in Feyd-Rautha to take the load off them, they'll cheer their rescuer. (26.208)
The Baron Harkonnen uses tradition as a political tool. First, he creates the tradition that Rabban is an awful leader. Then he breaks his own tradition by installing Feyd-Rautha. Clever, Baron, very clever indeed.
"They obey the preservation of the tribe," [Stilgar] said. "It is the way we choose among us for a leader. The leader is the one who is strongest, the one who brings water and security." (32.24)
Evolution meets tradition and custom in this quote. The Fremen traditionally choose leaders who will preserve the tribe in the same way that animal groups have leaders to ensure their own survival. The best part? No stupid bumper stickers.
[…] Jessica nodded, recognizing the ancient source of the [funeral] rite, and she thought: The meeting between ignorance and knowledge, between brutality and culture—it begins in the dignity with which we treat our dead. (34.69)
Jessica notes another aspect of funeral rites in relation to traditions and customs. According to this quote, it's what separates the cultural us from the more primal us still tucked within our brain.
Paul saw that Stilgar was too immersed in the Fremen way to consider the possibilities of any other. Here a leader took the reins from the dead hands of his predecessor, or slew among the strongest of his tribe if a leader died in the desert. Stilgar had risen to be a naib in that way. (42.83)
Stilgar is so wrapped up in the Fremen tradition that he can see no other way for Paul to become leader, even if it means his own death. Tradition and custom can be quite the taskmasters sometimes.