I don't think it's smart for us to just cede the whole realm of "ritual" to the religious. People (maybe instinctively) like ritual and make-believe, and that's OK. We already do loads of secular rituals, as people mention, in joking but it's true, our daily routines are little rituals. Good habits can help make us happy, I think it's OK to consider them "holy" from Wikipedia -
The English word holy dates back to at least the 11th Century with the Old English word hālig, an adjective derived from hāl meaning whole and used to mean 'uninjured, sound, healthy, entire, complete’
- related too, to my preferred term, "wholesome". My daily shit is more sacred / holy / wholesome for me than anything that happens in a church, it's part of my "earthly life" that the fundies hate so much. If I'm inclined to feel reverent and thrilled by the wonderment of my daily shit I'm going to go ahead and enjoy that feeling. Unlike bone-headed church ritual, laughing about the silliness of feeling awe-struck by a good poo, or whatever mundane "earthly" thing you can manage to get an awe-thrill from, the thrill and laughing at the thrill are not mutually exclusive like they are to the churchies. That's how you know you're doing it right. Mothra doesn't get pissed off that I laugh at the notion of believing in it, it's every bit as fun to believe in, knowing full well it's fake, and I don't feel afraid or guilty about wherever my daily level of Mothra reverence is.
Ritual is, I think, an innate part of our nature, it's a tool of the artist, it's part of our creative and imaginary life - it's only when we confuse ritual make-believe with reality, and put the force of the state behind it that things get ugly and wrong. Kids seem to be able to grasp this before wacky adults indoctrinate them with the religious double-think. In my family we talk about how it's fun to pretend-believe in gods, magic, fairies, dragons, etc. despite the fact that they are not real, they are exist in our minds. Santa is real in the same way that Love is real, they are in realm of the feelings, not real in the real world, where, as They Might Be Giants say so well "Science is Real".
I think this is part of being a freethinker - we are allowed any kind of games or shenanigans in our minds, there is no right or wrong in our minds, all thought and feelings are allowed, and each person is the final and only authority of what they want to do inside their own heads. I like to fake-believe in Mothra, it's fun for me, and harms no one. It seems to me that if blissing out on Mothra is my lazy way of meditating, and it offers me the real benefits (relaxation and all that) that the kooky religious get from their creepy rituals, I owe it to myself as a freethinker to make sure I have access to those same benefits. In fact I think I deserve those benefits MORE than do the religious, as I'm certainly not going to use my increased serenity, vitality, lifespan or whatever to stone my neighbors to death for adultery.
In the world that we all share, the real world, of course we try to be honest about what is real and what is not. Ideas we get from fake-believe are called ART, and they are a vital and wonderful part of human existence - we are allowed to take them as seriously as we like, but we may not expect or try to require anyone else to take them seriously at all, and anyone who does try to force or coerce anyone else's partaking in art is boorish, an anti-humanist bully, quite possibly crazy to boot, and certainly not to be trusted.
Art is fun, ritual is fun, it's one of the lures of religion, and we would be foolish and mean to deny ourselves the use of this tool - in fact, I think the more freethinkers use the art of ritual in freethinker-ish ways, well, that's a good thing. To offer a fun alternative to the "ritual kick" or comfort people get elsewhere, while also maybe shining a gentle light on how silly it is to be bullied by ritual.
So the answer to the question for me is "only if they want to".
I think carefully used ritual should not be seen as threatening to secular humanism, because we cherish values not with abstract intellect (our cerebral cortex) but our limbic system. In a sense I use meta-ritual, because my use of ritual includes rational discussion of the values and of why we affirm them using ritual.
An interesting study of the role of ritual in binding communities is found at Social evolution: The ritual animal
Rituals are a human universal — “the glue that holds social groups together”, explains Whitehouse, who leads the team of anthropologists, psychologists, historians, economists and archaeologists from 12 universities in the United Kingdom, the United States and Canada. Rituals can vary enormously, from the recitation of prayers in church, to the sometimes violent and humiliating initiations of US college fraternity pledges, to the bleeding of a young man's penis with bamboo razors and pig incisors in purity rituals among the Ilahita Arapesh of New Guinea. But beneath that diversity, Whitehouse believes, rituals are always about building community — which arguably makes them central to understanding how civilization itself began.
“This is the most wide-ranging scientific project on rituals attempted to date,”...
A major aim of the investigation is to test Whitehouse's theory that rituals come in two broad types, which have different effects on group bonding. Routine actions such as prayers at church, mosque or synagogue, or the daily pledge of allegiance recited in many US elementary schools, are rituals operating in what Whitehouse calls the 'doctrinal mode'. He argues that these rituals, which are easily transmitted to children and strangers, are well suited to forging religions, tribes, cities and nations — broad-based communities that do not depend on face-to-face contact.
Rare, traumatic activities such as beating, scarring or self-mutilation, by contrast, are rituals operating in what Whitehouse calls the 'imagistic mode'. “Traumatic rituals create strong bonds among those who experience them together,” he says, which makes them especially suited to creating small, intensely committed groups such as cults, military platoons or terrorist cells.
... used a previously developed database containing information on world cultures to explore the connections between frequency, peak levels of emotional arousal, and average community size for 645 rituals across 74 cultures3. As predicted, the rituals fell into two clusters: low-frequency but high-arousal imagistic varieties that were more common in societies with a smaller average community size, and high-frequency, low-arousal doctrinal rituals that were more established in societies in which communities are larger.
... also probing people's beliefs about how rituals work.
“We're built to learn from others,” she says, which leads us to repeat actions that seemed to work for someone else — “even if we don't understand how they produce the desired outcomes”.
Atran thinks that rituals could also feed conflict by turning the opinions and preferences of groups into 'sacred values' — absolute and non-negotiable beliefs that cannot be traded against material benefits such as money.
“Emotionally intense rituals have bound us together and pitted us against our enemies throughout the history of our species,” says Whitehouse. [emphasis mine]