Yes, but not in any conventional sense. I do not beleive in an anthropic god, nor do I place my faith in an afterlife. (Could be, but might not be an afterlife. certainly we dont know where the universe came from, what its made out of, or what conciousness is, but equally few of us have an direct experience of an afterlife, if any)
For me paleo, is about living in a human natural way, more than it is a mere diet. That included sleeping right, eating right, exercising, playing, having right relations with other human beings - and veiwing the world in the essentially vivid subjective manner that is true to the nature of our minds, and of our perceptions/senses.
The philosophy of phenomenology, such as Husserl, posits that all human knowledge is entirely confined to the subjective, and thus it is only the subjective that is true (approximately), and there is no such thing as objective. I agree with this. We are subjective beings, with subjective minds, and subjective senses - our experiences are strongly subjective.
This impression that science and skepticism can provid solid and certain knowledge, with which we can rest our whole view of the world on is a false impression. Science is great, but knowledge has severe limits, which is obvious if you think about the logic of scientific theory, or the nature of knowledge.
So I see the world as archetypes. This is a bit like animism. I see lifeforce as an essence, life as an essence. I see possibility, or chaos as an essence. I veiw the universe, as an expression of essential forces like these.
I also see the world as essentially unknowable, unfathomable, contradictory. And I see things as continous, or inseperable - connected. This is a bit like mysticism.
For me, this helps provide my life with meaning and context. I see this sense of meaning, connection to the world, as tied to my being paleo. They are both ways to exist naturally, according to human nature.
This fits with my human need for nature, with my human need for sunshine, with my human need for community and a need for real food. My body and being is designed with needs. One of those needs is a worldveiw that is natural and satisfying.
That said, there is some internal contradiction in the human mind, between human logic, and human superstition (the beleif in coincidences or co-occurence/synchronisity etc). I am not certain coincidences ever have particular importance or not, but it seems that beleiving too strongly in them is a deeply psychological related affair, and can contradict with a clear and logical veiw of events.
One has to be aware of what beleifs are bad crutches and which ones are good ones. Like "jesus" said build your house on stone, and not on sand. A strong beleif in intervention may lead only to disappointment when reality doesnt comply. Your better to have beleif that dont lean heavily on contingences, syncronisity or intervention.