What do guardians do?

[Jennah]

As far as I know, your choice is never referenced in the game, other than that bit in the eternal bond.
I picked Menphina; as the lore page says mooncats mostly worship her.
Zhloe runs an orphanage, "Menphina's Arms". When you first meet her, she talks about it. Zero opportunity to say "Hey, I like her too", or anything like that.

... it doesn't help that Rhalgr's the only one of the Twelve that's been at all relevant since 2.0.

[Iscah]

... it doesn't help that Rhalgr's the only one of the Twelve that's been at all relevant since 2.0.

Rhalgr hasn't been any more prominent than Halone was during Heavensward.

Each region has their own favoured deity, and most get mentioned quite often in small ways - and possibly by title rather than name. eg. the Matron (Nophica), the Navigator (Llymlaen), the Fury (Halone)

The Sharlayans favour Thaliak; the bard mentor prays to Althyk. The Temple of Qarn is dedicated to Azeyma. The lore for the zodiac constellations in the AST quest relates to all the gods.

There are lots of little references to them if you're looking.

[SenorPatty]

I think there was this bit in SB with Lyse?? talking about Rhalgr but other than that and the casual "Thal's balls!" that seems to be in many a Uldah denizens' vocab, there doesn't seem to be a focus.

[CaptainLagbeard]

Nowadays it's just flavor text for your character, it has no gameplay impact.

It used to very mildly affect elemental resistances, but they didn't really come into play even at the release of ARR... Don't know if they were more relevant in 1.x.