I have met people, online at least, who seem to get personally insulted at the idea that the gods might be treated and dealt with in a modern context. They will point to extant writings and say - see, that was written in xxxx, they didn't even have that thing you're offering back then! And why would they care about the task you're talking about? It isn't mentioned in the myths so - on and on. Their view is that the gods are ancient and unchanging and it is somehow sacrilegious to approach them on our terms or within our cultural world-view.
It is as if any changes, adaptations, evolution, etc. that occurred before the myths were written down were fine and natural, but once written they were set in stone for all eternity and no changes, adaptations, evolution, etc. is permitted from that point on. This, to me, always seems like an attempt to bind and contain the gods, to tie them safely into their stories and not have to deal with them as real beings or have them really intrude into modern life. It then becomes an archeological, intellectual, and literary pursuit rather than an active religion.
To me the history is valuable in the same way that knowing the background of a person you respect is valuable. I don't say the origin, because I don't believe they sprang full-grown into their myths. The earlier stuff just wasn't written down for the most part, and we are left with an arbitrary 'starting point' to our studies. Many people (not actual scholars, usually, but armchair folklorists and historians) dismiss unwritten variations and folk carry-ons of these tales as not canon, even when the variations come from the same geographical locations as the original tales. Only the ancient manuscripts hold the truth, and all investigation must start and stop there.
If the gods live in a truly separate place and have had no continued dealings with humanity since their tales were written, and simply shook their collective heads and withdrew from contact when we developed new ideas and cultures, then maybe they don't recognize chocolate or new incense blends or newer ideas about what constitutes morality or value. I prefer to think they approve of these new things, or maybe even inspire them. At the very least I think they accept them. I'm sure some ideas and inventions have fallen by the wayside, and these may even be the ones the gods truly did disapprove of.
This isn't to say that I think it's fine to offer a bacon sandwich to Aset when sharing a meal. If she has a dislike for pork that is strong and well-known enough for it to become a taboo then she is unlikely to have changed that. She is, however, likely to recognize a two-bedroom bungalow as a dwelling place, accept modern formulations of kyphi and natron, and whatever other earnest and respectful variations have developed over the ages.
Keeping the gods to their ancient ways and societies is fine if you simply admire them as artwork, but if you believe in them as living beings, and deal with them as such, then it is like insisting that a friend of twenty years standing is not allowed to change their hairstyle or their favourite treat. They may well not change their basic nature, most things/people/beings don't, but their ways of expressing themselves will move with the times. Trying to hold them back to a safe, stagnant representation of themselves that you found in an old book doesn't work unless they are 'just' stories and not real.
Most of the time, I would rather learn from a sincere practitioner than a precise historian (although I would truly rather learn from the two-in-one). The history is the easier to find on my own, and I am capable of reading any myth that has been translated into one of the languages I understand, and smart enough to know that those myths need to be related to the cultures from which they came rather than my own. They are snapshots in an old album, however, not up to the minute documentaries. The sincere practitioner is my go-to guy for what the gods are doing now.
Absent
I agree with everything you've just said.
One of the deepest fault lines in the Hellenic Pagan community lies between Neoplatonists and their Reconstructionist allies on the one hand, and more eclectic worshippers on the other. Hellenic Reconstructionist belief is often championed by Neoplatonists, who seem to hold that the Deathless Ones are distant and unchanging.
Their co-religionists, on the other side of the fence, believe that any attempt at strict Reconstructionism is an attempt to limit the Goddesses and Gods. They believe that the largely Athenian beliefs and rituals which have come down to us, have never adequately reflected the spiritual diversity of 'Classical Antiquity'. My superficial reading is that many of them (including myself) also refuse to discard Homer's concept of deity completely (Goddesses and Gods with 'human' qualities like emotions and aspirations).
Hence the clash between 'Fluffy Bunny' and 'Scratchy Badger'.
Me? For whatever it's worth, I'm somewhere in the middle.