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).
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."
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
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.
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.