It's that word "idea"- religions have ideas, of course; but there really is a difference between an idea and a creed. When we talk about a philosophical idea, I think we're talking about something more like a thesis- a simple suggestion about how some aspect of the world might be; a possible description of some aspect of reality. When I talk about Heidegger's "ideas", what I have in mind is something like his statement that "The meaning of the being of that being that we call Da-sein proves to be temporality". Personally, I don't really think this is an original idea- again, it sounds to me like Bergson got there first- but(!) I do think of it as an idea, and not part of a creed, and therefore not akin to an article of faith that you can ascribe to. I don't have any idea how one would be a "believer" of the idea that Being reveals itself through the dimension of time, other than perhaps just by not being a theist.
So, contrary to what I wrote, religions are not founded in ideas; they're founded in creeds. A creed is an authoritative summary of basic religious beliefs. In the articles of a creed, believers profess faith in mysteries that can really only be known through divine revelation. The word "creed" comes from the Latin "credo"- the first person singular, "I believe", which is the beginning of the Christian profession of faith. Catholics would know all this from the Nicene Creed, or the shorter Apostles' Creed, which are recited at every mass: "Credo in Deum Patrem omnipotentem, Creatorem caeli et terrae, et in Iesum Christum, Filium Eius unicum, Dominum nostrum, qui conceptus est de Spiritu Sancto, natus ex Maria Virgine, et cetera...
Or, more likely, "I believe in God, the Father almighty, creator of Heaven and earth. And in Jesus Christ, his only son, our Lord... et cetera."
Many of the other Christian denominations use the same creed, of course. It was essentially the first authoritative statement of Christian belief in the 300s AD. Muslims, of course, declare the shahada: "I bear witness that there is no god except Allah, and I bear witness that Muhammad is the messenger of Allah." My imperfect understanding of creeds is that you're not just supposed to say them after you've come to belief, but before- the creed "makes" you a believer, in basically the same way as something like the Pledge of Allegiance inculcates certain beliefs. My understanding is that the gift of belief is ultimately given by "grace".
(I'm not a practicing believer, so one can hopefully excuse my respectful, but no doubt flawed, summary of creeds. )
Cultures based in religious creeds we can refer to as credal cultures. At times and places there have been credal societies as well, although there are none at present in the "west". People who have been raised in credal cultures- believers, and there are plenty of them still around, tend- I think- to understand non-credal beliefs too often in terms of creeds. I'm sorry to be obtuse, but the way I understand intellectual ideas is that they're something the individual adopts and modifies to suit themselves and their needs. A creed, in contrast, is something that the person adopts and then modifies himself to suit the creed. A creed cannot change; however, ideas not only can change, but really have to change for an individual to make use of them in his or her life.
With Heidegger, his philosophical ideas eventually dovetailed with his repugnant political beliefs. For him, in my reading, it seems as if the philosophical ideas led him to the Nazi doctrines, aside from the racial theory, which he seemed to have disagreed with. But, otherwise, there were some strong connections there. I mean, it's not like we can say that Heidegger's epigones misused his ideas; he himself became a Nazi, and a thoroughgoing one at that.
But, his philosophical ideas were not creeds- they were not a doctrine that would necessarily lead to Nazism or anything else, aside from a headache! Most ideas are absorbed like food, we take what we can from them and expel the rest! In the process, they are transformed root and branch by us. I think credal peoples tend to look at non-credal cultures as being somehow akin to credal cultures- so, if you read a work of philosophy or a political statement, you run the risk of being transformed by it, as if it was a creed. But, even in the case of something like say "The Communist Manifesto", the work can be used, quoted, borrowed from, plagiarized, or rewritten without the slightest individual transformation taking place. Some people, of course, treated Marxist theory like a creed, with horrifying results, but it was really just a series of theories- ideas, in other words. Use them and your results may vary.
I tend to think of intellectual ideas as something like stops in a salad bar. You take a little bit of this and a little bit of that, and make use of them, or more often make no use of them. But creeds are an entirely different thing. And, often, when I read contemporary religious writers talking about the larger secular culture, I feel like they make the mistake of seeing the "culture", if there really is one any more, as being akin to either a variety of creeds or anti-creeds. But really its more like a plethora of fleeting ideas floating around like short-lit fireflies. Some of them are particularly stunning, but they never seem to last very long.
Some people call this cultural "nihilism" because it has no creed of belief. But I don't think the absence of a creed is nihilism. Because, ultimately, the non-credal culture doesn't simply descend into anarchy or the collapse of civil society. People seem to know how to behave decently and lovingly towards each other, even if they have no creeds. The Christian interpretation of this is that certain truths are written on the heart. The evolutionary theory is that certain moral ideas are "hard-wired". We seem to know how to be good people, and when we're not, it's pathology. Saul Bellow has a beautiful passage about this in his novel Mr. Sammler's Planet, in which the main character, an elderly Jew who has despaired of urban and cultural decline throughout the course of the novel finishes:
“For that is the truth of it – that we all know, God, that we know, that we know, we know, we know.”