First, go read Grayling's column at The Guardian.
Let me begin with three self-statements:
1. I disagree with many the social, theological, and hierarchical beliefs of the Catholic Church.
2. I believe gay people should have total equal rights in a free society, and that there is no reason gay couples should not be able to adopt children.
3. I am a strong advocate of separation of church and state and a secular society.
With those three statements, one would think I would agree with Grayling's column. We are looking at the issue from a similar place (albeit getting to that similar place in vastly different ways). But I do not. There are some problems in logic and tone. I'll pick out the quotes that strike me as intellectually unstable.
"It asks the prime minister to grant the Roman Catholic church's wish to continue being prejudiced and discriminatory in attitude and practice against a section of society whom texts 2000 and more years old instruct them to regard as abominations."
Being progressive does not mean that we have to think anything that is old is bad. Grayling's tone suggests that the very age of these texts should make us realize they are silly and should be abandoned. It is not entirely unreasonable to assume the opposite. Progressivism need not strike everything down and start from nothing--that never works. Progressivism can work within a culture for, well, progress.
"the Roman Catholic church (let us keep things in very sharp and very relevant perspective here, and remember what this organisation might equally well be called: viz. the Roman Paedophile Protection Agency) to be exempted from the law of the land so that it can continue its discriminatory prejudices."
Besides the intentially inflammatory label, is the implication that the Catholic Church might want to be exempted from prosecution for molestation charges? That they are so morally bankrupt on this issue that they should never ask for any exemptions from the law?
"In their pillow talk does she urge her husband to respect principles of equality before the law, and the human rights of all British citizens, in the face of attacks from narrow-minded bigots? Or does she think that personal choice of superstition trumps the law?"
I've always scoffed when people who disagree with the Catholic Church get called "anti-Catholic" or "bigoted." And I don't easily call anybody bigoted, given that I've been called one myself and it does sting. But let's just note that it's possible for somebody who labels all religious belief as superstition might have a fair dose of prejudices.
"The churches are making common cause in seeking exemptions from the law of the land. Grant one, and soon there will be another, and another; the self-selected coteries of believers will be islands of the exempted, as once they were in our history - above the law, protected by the law in doing what others will be punished for doing, because these latter do not have the modern analogue of "benefit of clergy"."
This is such an obvious use of the Slippery Slope Fallacy that I will not even comment on it.
"Notice this very central and salient fact. Even we who most robustly oppose the effect of superstition on public policy in society, and (separately but relatedly) combat the intellectual corruptions of superstitions belief systems, do not wish to stop cardinals, archbishops or their flocks from believing what they like and getting together in dark buildings to mumble and genuflect and roll their eyes up to heaven. Indeed we would act to protect their rights in this respect if others threatened them with laws to prevent them doing it, or ordering them to believe something else, even as we shake our heads over them or laugh outright at them for the absurdity of what they do."
Again with the intentionally inflammatory word choice. But based on what comes next, it seems Grayling is saying "We defend the right of religious people to believe what they want, to get together and worship as they want. But we do not defend the right to practice in life their religious beliefs."
"But we cannot accept that they should impose their beliefs and choices on the rest of society, or be immune from the law, or be allowed to perpetuate discrimination and bigotry, or be allowed to derail the progress that the rest of society is making towards fair, open, decent, and kindly dispensations of acceptance and inclusion."
Fair enough. I don't like when religious groups impose their beliefs either. However, I'm not sure that's what they're doing (they're not saying no gay people can adopt, they just don't want to help gay people adopt). Obviously England has different church-state laws than America. But if the religious group has an activity that doesn't hurt anybody (in this case, they're just refusing to help certain people, not actively hurting people), then the laws shouldn't require them to do things that are against their religious beliefs. My feeling remains that if a particular church doesn't like gay people, I won't like that particular church, but as a private entity that's still they're business.
In this case, much more than the church trying to impose values on the rest of society, Grayling is recommending that society be allowed to impose values on the church. Neither should be acceptable.
"This is a test case for whether we as a society are going to allow ancient superstition to dictate terms, or whether we are going to have to re-learn the lessons of the secularism"
So in order to not allow religion to dictate terms to the state, the state must dictate terms to religion? Can't they both not dictate terms to each other?
"against which the churches fought and fought, spilling the blood of millions: never forget how hard they fought to stop progress in these as in all other fields - which has got us as far (not far enough) as we have got today."
Often in history the churches--very famously and publicly--have attempted to impede progress. Too often. However, often churches have been at the forefront of progress, too. Churches have brought us a lot of good as a civilization, and it is unfair to selectively view history only in terms of the bad.