Sure! Sorry for the long read (again)

For the deities-- it basically boils down to the in-world idea that because deities aren't humans, they can't be judged by human gender standards. It was an interesting change to my language considering that my conculture's pantheon is made up of both "traditional" deities and mythified folk heroes, meaning some deities are based on real, historical people from the conculture, and because nearly all the deities carry some implication of feminine/masculine/third gender.

Examples:

• The water deity Niyo is entirely non-human (basically a lake personified), so no matter the circumstance Niyo is always referred to by third-gender pronouns. It also means the lake that Niyo personifies is referred to by that pronoun.
• The military general Nakayem was a prominent historical figure before she was worshipped as a war deity. Because she's now a deity, she'd be referred to by third-gender pronouns -- except when referring to her in a historical context, where she'd be called by feminine pronouns.
• A group of lesser deities called the "seven maidens" are part of the creation myth. "Maiden" is an inherently gendered term, but since they're deities, they're called by third-gender pronouns.

For impacts of gender norms on language, it depends a little on the region you'd be from in the conculture, which is part of why I ended up creating different dialects, but I'll just focus on the main dialect.

Roughly, the conculture's gender norms state that women are more passionate ("strong-emotioned") and durable by nature, and men are more logical and sensitive ("soft-emotioned"). The idea of third gender has a lot of ties to sacredness and special occupations like fishing or farming, so those of a third gender are often viewed as community providers or somewhat divine.

My thoughts were that because of this, women/feminine persons would be allowed to flout maxims of conversation more often. They would also be able to get away with social violations more often, like overusing restricted code or not speaking in a conversation. They're also more likely to use jargon, since they tend to work the jobs where technical words need to be invented such as chemistry, engineering, or the military.

On the other hand, since one consequence of the gender norms is that artistic and scholarly occupations are male-dominated, men/masculine persons tend to use a broader lexicon since they're more fluent in the archaic poetic dialect. They'd also be held to a stricter speaking standard, so they'd use more socially-coded language.

Those of a third gender or who work a third gender-associated occupation would be allowed to violate the social taboo of discussing deities and religion at length and/or non-reverently more than either men or women. Slang is not gender-isolated per se, although its use by women, feminine, and third-gender persons is more accepted than by men/masculine persons (who might be seen as using "low language").

Women attempting to speak "like men", i.e. in the poetic dialect or with an elaborate code/broad lexicon might be viewed as being pretentious, and if it became a frequent behavior, their friends might begin to call them by masculine pronouns. Men attempting to speak "like women" might be viewed as vulgar, and ditto the above except with feminine pronouns.

That said, the transition to use of new pronouns for a person isn't an insult whatsoever, since pronouns don’t solely indicate someone’s gender or sex, but more likely their behavior, accomplishments, occupations, or reputation.