[RPG] What role do deities play for non-Divine classes

One would think any good (and frankly even many Neutral) gods would have a place for opposition of black magic and foul sorcery. That's kinda like saying "who doesn't like murderers?" "Anyone but Norgorberites I guess?" is the answer. Even CN churches won't like it if there's enslaving/domination going on from the baddies.

Good type gods that are the most martial are Iomedae and Sarenrae. Gods with more of a craftsman aspect that might be Black Powder friendly are Torag and Abadar.

You'd do better to include what AP you're playing in and what kind of character you'd like to be like beyond the class details to get a more helpful answer. What part of Golarion? What kind of bad guys? If the answer is "necromancers" then suddenly Pharasma jumps up pretty highly in the choices, for example.

If you'd like a "Conan the savage who doesn't like arcane magic" feel, then the Kellid race and Gorum as a deity makes a lot of sense. Kellids from Numeria get some gun contact and would work very well for Reign of Winter (they hate White Witches), Iron Gods (from the area), and Wrath of the Righteous (from the area).

It Depends...

Plenty of examples can be found of characters being described in a non-mechanical ("fluff") context as worshiping, venerating, patronizing, idolizing, or giving offerings or tribute to multiple divine entities. On the flip side, while Clerics (for example) are not required to dedicate themselves to a divine entity, the game mechanics provide Clerics explicit options for the case where the Cleric is dedicated to a deity (singular) and the case where the Cleric is not. These options are implied to be binary:

A cleric's deity influences her alignment, what magic she can perform, her values, and how others see her. A cleric chooses two domains from among those belonging to her deity. A cleric can select an alignment domain (Chaos, Evil, Good, or Law) only if her alignment matches that domain. If a cleric is not devoted to a particular deity, she still selects two domains to represent her spiritual inclinations and abilities (subject to GM approval).

http://www.d20pfsrd.com/classes/core-classes/cleric#TOC-Domains

This leads me to believe that while no rules preclude a Cleric from worshiping multiple deities, any Cleric-specific mechanics that are based on the Cleric's association with a single deity would not apply to a Cleric lacking that one-to-one mapping.

Potentially, any worship-related mechanics involving a character whose class restricts her to the veneration of a primary deity could be subject to that restriction as well, but it's not as clear for characters whose class(es) lack this feature...

What about Non-Clerics?

The trait and feat combination specified as an example, however, is not restricted to Clerics. The rules of which I'm aware make no mention of generic prohibitions against the veneration of multiple divine entities on either a mechanical or a non-mechanical basis, though individual religions might. On that basis, and so long as the character is played in good faith (as it were), I can't see any reason to rule against the applicability of the trait and the feat in question. Note, however, that this may not be the case for all such combinations, and the question of non-Clerical mechanical worship is likely intended by the designers to be up to the discretion of individual GMs.

Note that the dev comments that I have been able to locate on the mechanics of worship all seem to be restricted to the context of divine casting classes, and are therefore not necessarily authoritative in a broader context.

James Jacobs: You can absolutely have a cleric who respects and admires and even offers prayers to multiple deities. Abstalar Zantus runs a pantheistic temple in Sandpoint, and is a prime example of this. But at the same time, he's primarily a cleric of Desna, over and above any other faith. He respects and reveres Shelyn and Gozreh and Sarenrae and Abadar and Erastil, and Desna doesn't mind and even approves of his prayers and faith in those deities... but his primary focus for his faith remains Desna. If deities were authors, you can like multiple writers but if you're a cleric, you have to have a clear favorite author. If you're an oracle (or more or less ANY other class, divine spellcaster or not), you don't. You can if you want, but it's not required. One of the ways that the cleric is defined as being a separate thing than every other class in Golarion is the fact that she DOES have a "favorite." http://paizo.com/threads/rzs2qufj?Polytheism-and-Golarion#48

James Jacobs: Again... because that's not how clerics work. Clerics get their spells from one deity, as a result of their devotion and loyalty to that deity. If a cleric could get his spells from any deity, then there's no reason to be loyal to a single deity. I really really REALLY think that oracles are going to do exactly what you want when it comes to a divine caster who doesn't worship a single deity.
http://paizo.com/threads/rzs2ktk1?Panthestic-Religion-in-Golarion#39

The remark about Oracles in the second quote seems to indicate that not only do these remarks only apply to Clerics (in this case) but that Oracles may be mechanically permitted to worship multiple deities.

Pathfinder Society

Specifically for Pathfinder Society play, the Society rules do impose a blanket mechanical restriction of a one-to-one character-to-god worship relationship for mechanical benefits, but this seems to me to be more for the sake of the way that Society play is structured than an indication of the intentions for the game outside the Society as a whole.