Did people with different beliefs choose to go different ways? Did it have an effect on how their religions and societies evolved? For example, I had the thought that people went towards the setting sun wanting to know, maybe subconsciously, where it went, so they were more focused on the future and fate. Then maybe the people that went east were more focused on the past and origin. Then I look at western religions like Christianity and how they're more about how this world is preparation for the next. Then eastern religions like Taoism are more about the flow of nature and intuition. Is there any truth to these kinds of thoughts? Thanks
First, it may be worth noting that the first species to "leave" Africa was Homo erectus. While certainly quite intelligent, it most likely had not developed a degree of cognition that he would associate with modern humans. That is, it probably hadn't developed a symbolic mode of thought that would result in the types of religious sentiments to which you are referring.
The migration of this species out of Africa was most likely induced by the nature of their mobility strategies. So to answer your question, where the sun rises probably did not influence where and how this migration occurred. The exploitation of previously uninhabited land the need to maintain low population densities most likely accounts for how the dispersal occurred.