Whether or not you are a religious person, religion has affected you in some way. For example, if you live in a Christian country it is very likely that you have developed some Christian morals and/or habits. If nothing else you likely know of some religious holidays for example, Christmas and Easter.
Religion and myth appears in fiction often; most of the time it is not really noticed. The Ranma ½ manga has a lot of religious symbols and references that most people don't really notice unless someone points them out. In fact if you know Ranma ½ mostly through fan fiction, Ranma (the character) does not seem like a religious person at all.
While Ranma's religion is unknown, I find it most likely that his religion is a mix of Shinto and Buddhism given what is seen in the manga. Ranma can be seen praying in a few story arcs. Most visible example is his praying during the Koi-rod story line, though he can be seen praying on a few other occasions as well (praying at his family grave comes to mind). Ranma believes in both the Kami and in there being an after life. Though unlike most people his belief is not based solely on faith. He has seen the power of the Kami (Shinto wards have actual effects) and met the Kami (the Oni is a type of Kami and so was the divine horse - of the 8 million or so Kami animal types are the most common). He has met spirits and ghosts, seen the shores of Sanzu (the Buddhist river of the dead), and seen a ghost enter into heaven.
Some of the other religious imagery seen in the manga:
-Kasumi wears a crucifix.
-Nabiki wears a crucifix during the initial date in the ten yen date arc.
-The Tendo dojo has a Kamidana (small Shinto shrine that is hung on a wall).
-The Tendo's have a Butsudan (a Buddhist shrine for in the house).
-The person that waters her front yard, getting Ranma wet, is practicing a form of misogi - a Shinto purification ritual.
-Kodachi goes to a Catholic School.
-One of the competing plays during the Romeo and Juliet story arc was doing a play involving Jesus Christ.
-Shinto and Buddhist priests are seen several times in the manga, as well as Taoist Monks.
-Ranma goes to both Shinto and Buddhist Shrines.
-Religious holidays are shown in the manga for example, Christmas and New Years (New Years is a religious holiday because the 108 bell ring during the ghost cat storyline is a Buddhist celebration with each bell rings represent 108 elements of bonno, defilements, or Kilesa in Sanskrit, which is said people have in their mind).
-Volume 37 and 38 both show aspects of Shinto and Christian weddings (Akane is dressed in Shinto wedding garb and Christian style wedding dress respectively).
-The battle versus Herb takes place at and destroys Mount Horai which is a mythical mountain similar in nature to Mount Olympus of Greek Mythology.
-Akane in a dream sequence chases Happosai with a cross.
-Sanzu the Buddhist river to the afterlife shows up a few times (Noodles of strength arc, Herb arc, etc.)
-Rouge cursed form is a goddess/demoness in Buddhism, Shinto, Hindu.
-Tea Ceremony has origins involving Zen Buddhism and Confucianism.
-Martial arts has many ties with religion including: Hinduism, Buddhism, Daoism, Confucianism and/or Shinto.
-Ikebana (Flower arranging) has roots in Shinto and Buddhism.
Two religion inspired things that deserve singling out:
The Orachi arc is a retelling of the Susano (high ranking Shinto wind god) battle versus the Orachi. The Ranma characters play the part of the god, the broom being used as a stand in for Kusanagi (legendary sword), and the cross dressing is used as the trick.
The second thing that deserves singling out is Saffron. Mainly whether he is a god or not. Going by a monotheistic religion such as Christianity, Judaism, and Islam; no Saffron is not a god. Going by polytheistic religions such as Shinto, Voodoo, and ancient religions (Greek, Roman, etc.); then yes Saffron could count as a god. So really it is entirely up to the readers interpretation and can be taken either way, though by Shinto, the predominate religion of Japan, he would be considered a Kami. Saffron's comments are about ascension and rebirth which is what happens when a being transcends from mortality to either demi or full blown godhood and his pagoda has symbols of divinity on it. Though Saffron more resembles the western phoenix than he does the Japanese type.