“Cynicism.”
There are many forms of intolerance which have to do with religion, but they don’t seem to fall into one neat category.
Those who are, for lack of a better word, anti-faith (belief in anything other than provable facts makes you at best an idiot, at worst an enemy).
Those who are particularly anti-Christian while not in favor of any other faith either. Could apply to other singled-out religions.
Those who belong to one faith but are bigoted against other faiths, or perhaps just one other faith (anti-Christian Muslims, anti-Muslim Christians, etc.)
Those who hate co-religionists who open their eggs on the small end instead of the divinely ordained large end.
It is possible each of these might require its own name.
Though isn’t this about sects within a religion (hence the name) not different religions. So it is used in places like Northern Ireland to describe prejudice and violence between Protestants and Catholics, or in Iraq between Sunnis and Shiites but not to describe prejudice between religions.
As it was Jonathan Swift who thaught us about the bitter factional dispute raging between those who break open their eggs at the little end (Little-Endians) and those who choose the big end (Big-Endians) the right word would be Swifties or Anti-Swifties, I guess. Oh, wait…
You got the method wrong anyway, it is the short end that is divinely ordained. Or was it sunny side up?
ETA: The word I believe the OP Cardigan is looking for is radical humanist.
Divine was obviously a dangerous heretic.
Paging @Yookeroo …
I don’t think this works. It is possible to be a secularist and not be against religions which don’t try to control other people. The term I’ve heard is “anti-theist” which says that all religion is not just wrong but harmful. Even Unitarians.
Famously and influentially:
Within denominations, anti-clericalism can refer to the sentiment that God does not speak to or direct only those whom the denomination has ordained. It recognizes that the laity has a place in denominational structure or function. IOW, anti-clericalism challenges the assumption that only those ordained posses authority in the denomination.
Cardiganist…you silly guy
Dan
Glad you liked it. 
But I’m a gal. 
Or it could mean that religionists are somtimes indoctrinated.
Do not understand what you mean.
Some of us opposed to the intrusion of religion in social, legal and political circles take into consideration that some religionists have been indoctrinated by those same forces. That doesn’t make them idiots(or worse).
It just makes them human.
The bit you quoted is literally exactly that: a secularist who is not against religions, as long as they don’t try to control other people.
Just for completeness there’s “anti-ecclesiastical” which is anti-church. Seems like you’d hear that more in a society where so many say “I’m not against religion, just organized religion.”
Monkey see monkey do, When humans decided it wasn’t a good thing for humans to model themselves after other humans, they created God. Thats not to say that God doesn’t exist, but we had to create a version we could comprehend. Religion is more about giving ourselves an identity we can carry throughout our lives and be happy with it. A person who doesn’t like themselves doesn’t always behave well. Obviously not everyone needs this but there are a lot of us who do.
Still clever, and I’d like to imagine I’m nearly as clever. Thanks
Dan
I tend to use “bigotry” for most of these.
Antidisestablishmentarianism = let’s keep government subsidies flowing to the Church of England. We do so many good things, and put up with so many bad vicar/knicker jokes