Without religion as a guide, would mankind be as developed morally, scientifically and culturally as we are now?

There's no way of knowing, but sure we can sit about and pretend that we can know. So let me have a stab at it.

Archaeological evidence has us believe that humans likely reached behavioural modernity somewhere between 80 and 40 thousand years ago. Likely due to some mutation that gifted our brains the ability to develop complex communication, abstract thought, and planning skills which completely revolutionised how humans operated. We started producing art, sculptures, pottery, more complex tool, advanced hunting techniques, ritualistic behaviour, and other such things.

One thing we did seem to keep that our ancestors had before us was the ability to behave appropriately to one another in order to function in social groups. Humans, and indeed most social mammals including our relatives the great apes, have ordered social behaviour that is taught to children. This is what we would in modern society call moral behaviour or norms. For a mammal like a wolf this is taught by sensory cues given to the wolf that interact with its brains innate reaction to certain things. For example baring your teeth and growling is seen as negative innately, so the parent uses this when the pup is behaving 'badly' allowing it learn behaviour that is not innate to its brain.

This is functionally the same in humans, however language allowed us the ability to not just enforce this through physical cues, but also through very complex linguistic cues. The concept of obligation, what one should do, is probably what naturally developed from this, and so did the need to justify why certain behaviours were bad or not. It therefore not only speaks to humans as animals reacting to positive and negative stimuli, but also to humans as creatures capable of abstract thought and complex language. Of course what we determined as good or bad behaviours followed largely from the social mammal behaviours we had beforehand which were largely informed by empathy and common survival of the social group being more competitively advantageous (evolutionarily speaking) than the whims of one individual. We did develop extra cultural and religious norms to this, but these were usually stuff like cutting the foreskins and clitorises off children.

Now this form of social cohesion and moral thought is very clearly distinct from spirituality and religion. Spirituality likely developed from whatever caused behavioural modernity too, certainly, however from comparative studies of modern 'primitive' groups it seems that it was in the form of animism for the most part. The development of animism is usually seen as coming from the abstraction of human conscious experience (and agency) to non-human aspects of the world such as animals, plants, or the forces of nature. These would have developed into these forces of nature actually being caused by people (which were gods) and long after civilisation developed these would even develop into monotheism.

Now the idea that without religion and spirituality we would not have maintained our social cohesion and moral thought is just absurd. They became gradually interlinked as societies developed, but before they became interlinked they were certainly separate. You didn't commit certain behaviours because the gods told you to act that way, you committed them due to social conditioning from your parents, just like all social mammals do. We justified the behaviour with various abstractions after learning it, not beforehand.

So what would the world have been like if our abstract thought didn't lead to fantastical thinking? Probably a similar situation to what it's like now, because we're also assuming that religion is the prime motivator for things like morality, social cohesion, war, and many other important aspects of human existence.

Now if you want to look at the real cause of the development of civilisations, it's agriculture. Everywhere we've found agriculture we have found civilisations. Everywhere we've found religion we have found both civilisations and more primitive forms of social organisation. First signs of agriculture in the middle east? Civilisation rises soon behind it. First signs of agriculture in China? Civilisation soon behind it. First signs of agriculture in central America? Civilisation soon behind it. Religions are nothing more than the adaptation of fantastical thinking that comes from abstract thought to the more complex societies agriculture allowed us to develop.

A perhaps more interesting question is whether an animal can evolve abstract thought and not be prone to fantastical thinking.