All of these things are huge on the Horde, so I don’t know where this comes from.
Law & Order is not unique to the Alliance, the Horde has this as well. You must accept the law of the Horde to become a member of that faction.
But under the Alliance, domestically, everyone gets to rule themselves. 100%.
The Council of Three Hammers rules Ironforge, and only recently did the Dark Iron join the Alliance… So how did that work before the Dark Iron were in the Alliance? Was Ironforge not run by the Alliance? Anduin has no say what the Night Elves or Dwarves do. The leader of the Alliance leads on the military, not the people. Gnomes, Draenei, Night Elves, Kul Tiras, the Dwarves, and Gilneas are all run by their own laws and customs. Just like the Dwarves of the council. They ran themselves but of course the Wildhammer and Bronzebeard used their majority to sway the Kingdom of Ironforge.
Tradition is easy. Of course the Horde has a lot of tradition. So does the Alliance but I see the Horde as more of a traditional society. They have a very elder-focused tribal way of things but that’s just my own perception and not rooted in the lore that it’s more of a Horde thing. So it’s hard to say exactly who has more cultural tradition.
When it comes to faith… The Horde is all over this.
From Trolls having their Loa religion and being extremely devout Voodooists, to virtually all Tauren having a religion in either ancestor worship via Shamanism and now introduced to them again with the Light. Then you have the Blood Elves who among them have many Light Followers and pilgrims who visit the Sunwell from all over Azeroth.
The Alliance definitely has religion beat on the Horde though I’ll give you that. The Draenei are very attuned to the Light and only some of them follow Shamanism. Then you have the Church of the Light being a staple in Human society except for Gilneas and Kul Tiras. But Harvest Witches in Gilneas with an introduction to Druidism has kept this society very different from the Light focused Stormwind Humans and the Shamanistic society of Kul Tiras.
Both factions have races with seemingly large atheistic non-religious members. Void Elves, Nightborne, Orcs, Goblins, Forsaken, Dwarves, and Gnomes. Horde has more of them so it seems yep, Alliance is more religious but not by much.