Depends how you define religion, no? Once upon a time Victoria banned Scientology as not a religion, but it was overturned by the High Court. And by some definitions secular humanism is a religion. For some it includes regular scheduled activities that are "church-like" (for example, would you want to exclude those going along to Sunday Assembly?)
Totally off-topic (forgive me)
Spoiler
Not to point out the elephant in the room, but secularism is anything but religious.
I've heard this argument before, and it's not particularly convincing, especially when you start hearing people saying atheists are religious. Which is just strange and shows a total disregard for what consensus says religion constitutes. I'll try to explain what I mean by that.
Religion isn't equal to beliefs or holding a belief system, despite what some inaccurate dictionaries may state. It does involve having beliefs, but that's not what it is. It's also not a routine. Like, going to church doesn't automatically mean that you're Christian, for example. It may certainly suggest that perhaps you're religious and associated with christians, but that evidence alone isn't enough to say that you're Christian. It's also (sadly) not personal, because then it would totally defeat the purposes of having a religion (having objective morals etc). It's personal in a sense and a little touchy-feely. It just becomes incredibly relativistic, when we say people decide what religion means to them.
Religion is almost always (I say 'almost' because 'qualifiers' haha) tied to the supernatural or the superhuman. This is probably why a lot of people have problems with religion because there is always some unfalsifiable element universalising their morals and therefore justifying their actions. How it's organised into distinct groups and sects is as much a theological as it is a social phenomena.
One thing I will definitely address is the common misconception people have of those holding a belief system that contain no supernatural deity eg. atheism or secular humanism etc. And this is where the 'secular people/atheists are religious' arguments come into play.
I'll use atheism for simplicity. I know this may sound contradictory to what I was saying above, but atheism actually isn't an ardent belief in the non-existence of gods from what I've gathered in conversation. How I see it, it's an expressed skepticism toward theist religions because they haven't provided the burden of proof that their deity/deities exist(s). And I'm sure with secular humanism this is where they're coming from as well.
The best explanation I've heard was that atheists are without a god or without religion, but they don't necessarily assert that 'there is no god full stop'. Some do, but I don't believe this resonates with every atheist. In fact, a lot of public atheists like Stephen Fry have expressed that they'd happily convert to religions if they were given substantial evidence that a god from a particular religion truly exists beyond doubt. There seems to be a particular emphasis on their disbelief with what many religions assert to be sensible and why they the religious folks think everything is the way that it is. Not on the fact that there is no god/gods etc.
Now, most people stray from using the word atheist to describe themselves, because of the associations it has with equally dogmatic people asserting in the definite non-existence of supernatural deities. They go for the word agnostic to describe themselves, but my only problem with this is that agnosticism doesn't describe their position on whether or not they are a theist/whether or not they have a religion. It just says this is what I know rather than what I believe.
More likely than not, the word they're going for is: an atheist who is also agnostic as opposed to gnosticism, or agnostic atheist. Which in my rough estimate, would pretty much sum up the belief position many atheists themselves hold.
I could be wrong, because I've consulted at least 50 definitions, and some have asserted that atheists believe that there is no god. But I don't believe this is the definition which a lot of atheists use to describe their position. Or at least, it's not what I'm hearing when I listen to what they're saying.
Atheists are irreligious, precisely because they're not a follower of any religion, and I don't think this makes them religious at all. Because to be religious, you must necessarily have a religion.
*sorry very off-topic. But I've just heard this waay too many times and thought I should chime in haha I'll show myself out.
Totally off-topic (forgive me)
Not completely off-topic.
Spoiler
Peter, I'm an atheist and I agree with most of what you say. I tend to use the definition "A person who lacks belief in the existence of any gods". Which is completely not a religion. On another day I might have (and probably have) written similar to you.
However, in this context I think it's slightly different, because the "chaplain" debate is using "religion" as a proxy for "being able to give moral guidance". Similar has come up in the prison system: If you let a religious person access a chaplain of their chosen religion, can you really withhold from an atheist the advice and support of a secular life coach / councellor, however defined? If so, you are either giving a special privilege to some for holding a religion, or discriminating against some for not holding a religion.
Secular humanism is different from atheism (in my view) because it makes positive assertions about the world, and has axioms for determining what is right or wrong, good or bad. I don't call myself a secular humanist, though I suspect in many areas my moral code would overlap with it. But it goes further: I am told some brands of Buddhism have little or no supernatural, and I have seen definitions of religion (serious discussions, not dictionary definitions) wide enough to include secular humanism, strong nationalism, and Marxism / communism / socialism (yes, I know those last three are not even close to the same, but they are often grouped). Call them ideologies rather than religions if you prefer, but they can share some of the same markers: dogmatism, taking over a person's entire life, dictating morals and life practice, defining the highest possible good or purpose to life.
And if you're not happy to accept any of that wider definition, then we're back to "religion, narrowly defined, is a poor marker for morality". I'd accept that statement, which as I read it was OP's original point.