I also think your distinction between atheism and secularism is sleight of hand. Secularism unsupported by atheism is nonsensical. The reason why a secularist objects so strongly about the extension of religion into the public sphere – and even its private practice – is because its adherents are delusional, and, using your own words, imposing a delusional set of values and practices on others.I actually find this quite extraordinary. Hutton seems like an intelligent and well-educated man, but here he is utterly confused - and it's not Dawkins' fault but his own.
Nor do I understand what you mean by religious secularists: it sounds like "expansionary fiscal contraction" – a contradiction in terms. Martin Luther King and Gandhi certainly had secular ambitions, but their inspiration and inner strength came from religious conviction. You've made your reputation by being one of the country's most articulate atheists. Don't muddy the waters!
No, there is nothing at all that is "sleight of hand" about distinguishing between atheism and secularism. Atheism is an informed absence of belief in any gods (or, if you are thinking of a stronger kind of atheism, a denial that any gods exist). Secularism is the view that the state, or the government, should not be enacting laws and making decisions on religious grounds.
You can be an atheist without being a secularist (you might not personally believe in God, but you might think that it is good for society if the state imposes traditional religious beliefs). There may not be many people like that, but there are some.
You can also be a secularist without being an atheist, and indeed while believing in some religion or other. There are many such people; in fact they are probably the majority of secularists in many countries.
It's going to depend on your theological standpoint, but many theologies allow the view that it is not the business of their religion to try to get the state to impose true religious views on non-believers. If that is your position, you can certainly accept the secularist coin view that it is not the business of the state to be identifying the true (or most beneficial) religion and then imposing its standards on everyone,including non-believers.
Hutton says: "The reason why a secularist objects so strongly about the extension of religion into the public sphere – and even its private practice – is because its adherents are delusional, and, using your own words, imposing a delusional set of values and practices on others."
Well, not really. I don't want someone else's values and practices imposed on me whether these values and practices are "delusional" or not. I don't want them imposed on me because they are not my values and practices. All religious believers, as well as atheists, have a stake in living under a political system that allows each person a great deal of latitude to live in accordance with her own beliefs and values, and engage in her own practices. It is better all round if the state does not get too far into this, and most of us could agree that the state does not do a good job of it. For a start, it should not be identifying and imposing the "correct" religion.
I said "a great deal of latitude" because the state does, in fact, require some things, such as that we not murder each other, that we look after our children, and that we pay our taxes. But modern secular states do not impose comprehensive systems of thought on their citizens, and they do not impose specifically religious standards of morality (or at least they have tended to move away from imposing such standards). If these states have a legitimate interest in imposing a morality at all, it is a rather minimal one related to avoidance of worldly harms and requiring some basic mutual cooperation. That leaves all sorts of other decisions to the individuals concerned. Hence such catchphrases as, "Don't like abortion. Don't have one!"
Indeed, early secularists such as John Locke tended to be Protestant Christians rather than atheists. Secularists these days can belong to almost any religion, though it's true that Muslims and Catholics (at least the higher clergy, not necessarily ordinary Catholics) can have a problem with secularism. Those religions have, historically, been particularly unwilling to draw even a conceptual line between religious and political authority.
Getting back to the Hutton/Dawkins debate, Dawkins is not muddying the waters at all. What he has to say is clear and accurate, while Hutton seems to have a bizarre, incorrect, and ahistorical idea of what secularism is all about. If someone like him can be this confused, we clearly have a lot of work to do.
Finally, I do realise that there are some grey areas, puzzles, etc., here for philosophers to discuss. But that's not what Hutton is talking about. He misunderstands the nature of secularism at a very basic level.