The late Psychologist, Carl Jung, developed the thesis of the archetypes of the collective unconscious. In more modern computer terms, the archetypes are genetic based personality firmware of the brain, which underly human nature. These are common to all humans and define us as a species. All humans, regardless of culture, are basically the same in terms of human nature. Human nature is deeper than culture.
For example, we all fall in love at one time or another. When active, this firmware is projected onto the beloved, to make the beloved appear better than real.These dynamics, were conscious in ancient times and were attributed to a goddess, such as Aphrodite. Polytheism essentially was an ancient way of mapping out the ancient personality firmware, through projection.
Monotheism is more concerned with the center of the collective unconscious. This center is called the inner self by Jung. The inner self controls all the firmware; masks of the inner self. While polytheism breaks down the firmware into its individual specially components, some of which are blends of more that one firmware. The Centaur, is half horse and half man or part instinct and part a product of culture.
The characters of mythology were real, in a sense that they were a projection of something that was inside the human psyche. The mythology projection was like of a cultural mask, given to a real thing that was similar to software-firmware code of the brain.
As an analogy, you can feel your heart beat, to know there is a heart in your chest. However, if you never saw a real heart up close, you might try to image what the heart looks like. Someone, in our group may come up with an imaginary image of the heart, that appeals to the group. This image is not real; in terms of anatomy, but it is based on something that is real, that we all can sense, by the beat and location of the beat. This paradox of real, but not real, is why we have these debates, since both sides are part of the truth.
Worship of the goddess Aphrodite, to use an example, was essentially using time proven cultural command lines, to help trigger this particular firmware. Falling in love is not something you can do by will or by choice. It happens on its own, time to time. This is because the firmware lies deeper in the psyche, than the ego, and is triggered by the inner self, as needed.
The command lines of worship were a way to induce the firmware; hoping the goddess would appear; so we can induce or amplify the love. This is no different from the athlete, doing his ritual before the game, so he has a good game. It seeks the help of the gods; unconscious, which control the outcome of sports and allows amazing shots for the fans.
Modern humans, as a whole, do not all collectively personify the firmware, as in the days of old. However, we still do the same thing. Each person may have their personal ritual of worship for firmware induction. The correct command line is like a coin, we put in the juke box of the firmware, so the inner self will play the song we need. The old couple may renew their vows of marriage, so the goddess will intercede. Deep inside the operating system of the brain, this ritual triggers the jukebox to play once again. Personification or reinforcing old memory, helps one to focus and push play. It is all good.