One cannot do a study to compare a belief system to another one and call them both religions unless you detail the tenets of those belief systems. These are the statements which you MUST believe in to belong to that religion. Without agreeing to them all, you could be kicked out of that religion as a Heretic. I agree that the four functions are common to many religion but for example some religions have few rituals. Cults have what we would think of as very odd "meaning and purpose.

Meaning; Nature's laws is the only so called religion I can mostly understand. Bio organisms and individualism finds better meanings. Centroism has very little meaning to me.
Purpose- I've alway set and sacrifice my purpose in life as I go along,
Community I love science and critical thinking which some are great at here Although many here have influenced by political and corporationism science guiding them. Artist are my strongest tribe.
Rituals- My strength is not in words, being here helps my visual pictures and creative concepts for greater expression in my sculpture works. Agnostic.com are very hard critic's . I get too many compliments on the physical outside world, yet learn less from it.

I’m a little late to this, but I am not much of a fan of the “Nones” categorization. First off it’s one of those privative catch-all terms like “invertebrate”. Knowing an animal is excluded from the vertebrate group doesn’t yield much information as invertebrates are a disparate group.

The key lacking with “nones” is formal religious affiliation. I recall atheists locking on to this category with glee. Yet: “However, a new survey by the Pew Research Center’s Forum on Religion & Public Life, conducted jointly with the PBS television program Religion & Ethics NewsWeekly, finds that many of the country’s 46 million unaffiliated adults are religious or spiritual in some way. Two-thirds of them say they believe in God (68%). More than half say they often feel a deep connection with nature and the earth (58%), while more than a third classify themselves as “spiritual” but not “religious” (37%), and one-in-five (21%) say they pray every day. In addition, most religiously unaffiliated Americans think that churches and other religious institutions benefit society by strengthening community bonds and aiding the poor.

With few exceptions, though, the unaffiliated say they are not looking for a religion that would be right for them. Overwhelmingly, they think that religious organizations are too concerned with money and power, too focused on rules and too involved in politics.”

[pewresearch.org]

Probably a bit out of date. A majority believed then in God. A large subset were still “spiritual”.

The lack of affiliation itself might be a trend, along the lines of Putnam’s “bowling alone” notion. People seem to disaffiliate from formal political parties but are still politically minded.

It’s your binding of ideology and religion that’s kinda troubling in itself. Seems a subtle way to brand “the woke” or SJWs as religious, a tactic I’ve seen used by the antiwoke. Since just about any social media discussion winds up sucked into that moral panic tractor beam framing any more, it sure seems where this is headed.

A quote from the book:
"It’s the story of how more and more Americans—and particularly how more and more millennials—envision themselves as creators of their own bespoke religions, mixing and matching spiritual and aesthetic and experiential and philosophical traditions. The Remixed hunger for the same things human beings have always longed for: a sense of meaning in the world and personal purpose within that meaning, a community to share that experience with, and rituals to bring the power of that experience into achievable, everyday life. "

The syllogism falls at the final hurdle ie. it is a non sequitur.

1. Many ideologies are religions because they entail meaning, purpose, community and ritual.

2. Many who are unaffiliated to religion also seek meaning, purpose, community and ritual.

3. Therefore religion does not require gods.

the above ASSumes i want or need a "meaningful" life......

Religions have doctrine; dogma or laws. Religions occur when people share the same belief and someone organises things.
A Shared belief will often have a shared purpose. That is community.
Nones have no doctrine. Religious like fever is displayed by some with shared purpose but are they religions or fleeting cults?

I think anyone who truly understands the nature of reality and meaning/purpose in relation to metaphysical properties the way religions/ the religious explain would wholly disagree that a "none" would meet the first two requirements.

This all seems very true on the surface but then exceptions creep in. For example, a person can be in church and hear the minister claim that we all believe alike. Those of us in this meeting all believe the same things religiously. In private talks with any of these people you find that it is not true. This is also the reason there are so many religious denominations.

Religion by definition involves binding oneself to a set of ideals. The very word religion come from the same root Latin word as ligature, "ligatus" to bind and the Latin prefix re- to redo, to go through again, hence weekly rituals to re-tighten the binding of one self to an ideology. So as far as this goes, what you present is a fair definition of a religion, other than it lacks a supernatural element and a requirement for faith which is a priority for almost all religions. Communism for example meets ALL the requirements for a religion other than that its object of faith is an ambition, a belief in a future conforming to the ideals of Marx and the communist patriarchs and it outright rejects the supernatural (only room for one boogie man in the commie camp).
So without that supernatural element an ideology can and Does have a hard time selling itself as a religion.
Atheism I would argue, meets none of the requirements, it is simply an intellectual standpoint, in that to be atheist all that is required is an opinion that the concept of a god or gods existing has spectacularly failed to meet its burden of proof and so can be logically rejected as not even worthy of being considered an hypothesis.
It seeks not to give life meaning
It offers or delivers no perfect method for living a life, not offers any meaning for life.
There is no weekly or periodic rebinding neither compulsory or even voluntary ritual
and other than expressing loosely connected ideas based around (lets face it) worrying about the dangerous effect religion is having on the world there is no official or even casual atheist community other than perhaps a few activist organizations such as the FFRF and the Satanic temple who enjoy winding up bigots and throwing stumbling blocks in to the way of their pious pontifications and parading.

Sure, why not? Religion, after all, does not necessarily have to be about belief in supernatural forces or beings. The word "religion" comes from the Italian "religgio," meaning re-linking, as in finding the (lost) connection between one's self and his/her/their cosmic origins. In this sense, science can be considered a form of religion.