Above: Pat Morita in the godawful film version of Even Cowgirls Get the Blues, which omits the Clock People storyline entirely. For your own sake, read the novel instead.
The Clock People manage their anarchism (if that is not a contradiction) simply because they have channeled all of their authoritarian compulsions and control mania into a single ritual. It is clearly understood by all members of the community that there is no other ritual, no other required belief than this one—and, furthermore, that they themselves created the ritual: they have no silly superstitions about gods or ancestor spirits who hold this ritual over their heads in return for homage and/or “good” conduct.
Ritual, usually, is an action or ceremony employed to create a unity of mind among a congregation or community. The Clock People see the keeping of the clockworks as the last of the communal rituals. With the destruction of the clockworks, that is, at the end of time, all rituals will be personal and idiosyncratic, serving not to unify a community/cult in a common cause but to link each single individual with the universe in whatever manner suits him or her best. Unity will give way to plurality in the Eternity of Joy, although, since the universe is simultaneously many and One, whatever links the individual to the universe will automatically link him or her to all others, even while it enhances his or her completely separate identity in an eternal milkshake unclabbered by time.
Thus, paradoxically, the replacement of societal with individual rituals will bring about an ultimate unity vastly more universal than the plexus of communal rites that presently divides peoples into unwieldy, agitating and competing groups.