In this poem, there are several examples which support that people continue with customs just for the sake of doing so.
First, the speaker notes that the wall they meet to repair isn't a necessity:
He is all pine and I am apple orchard.
My apple trees will never get across
And eat the cones under his pines, I tell him.
If the wall kept livestock out of his neighbor's pastures or if the wall kept their varied livestock from mixing, the wall would serve a purpose. Since this isn't the case, the speaker questions why the wall needs to be repaired at all. His neighbor has no real answer except that "good fences make good neighbours."
Second, the author notes that his neighbor makes his repairs "like an old-stone savage armed." There is a sense that it has always been done this way, reinforced in the closing of the poem when the speaker notes that his neighbor "will not go behind his father's saying." Because his father built and repaired walls, the neighbor will continue the tradition.
Although "slave" might be a strong word to associate with this sense of ritualistic behavior, there is support that people have tendencies to keep doing things the way they have always been done, even when it doesn't make much sense.