Religion taught us (in no particular order):
Ok, I'll try to answer those posits in no particular order then also. And I will qualify my examples as rudimentary natural abilities in many animal species.
The days of the week, months of the year, when to plant and when to harvest.
Termites have practiced agriculture of planting, tending and harvesting for ~500 million years.
The value of a day of rest because G-d him/herself valued it
That's nonsense. All living things (except perhaps for sharks) require rest at regular intervals. Humans just institutionalized it for practical purposes. Even trees and plants go seasonally dormant.
Koko the gorilla was able to read and write and had a vocabulary of some 2000 words, just not in human symbolic language, but that is beside the point. I can't read Chinese symbolic language either. Koko even named her Manx kitten "All Ball" because it had no tail and looked like a ball, which was a common play toy for her. This is advanced abstract thinking, IMO.
Lemurs, all apes, all monkeys, crows, fish know the difference between "more and less" of a variety of objects, even if these objects are mixed in shape and color. Humans have just symbolically formalized the different values. But bees are able to tell the hive where and abundant supply of flowering plants may be found.
To issue currency, and to mistrust those who learned to count it
I'll give you that.
To enforce morality and social contracts with the rule of law, pay taxes to support enforcement
Ever watched an alpha male Chimpanzee enforce his laws of obedience to him and his right to first choice ?
The greatest armies that ever lived can be found in the driver ants and locusts.
The traditions of honoring our dead and burying them
Elephants honor their dead, but they don't bury them.
The mistaken and misguided idea that our enemies in this life or the next have any lesser value than our own.
I'll give you that.
I think that about covers it. Any regrets about these traditions?
No, but you missed two important assets, that of generosity and cooperation, both which can be found in the Bonobo chimp.
Notice that some parts of religious tradition (plant, harvest, read, count) pertains to acquiring knowledge, while other parts (war) foster ignorance.
The regularities in our ecosystem has been teaching living things for ~500 millions of years. Even a slime mold has a sense of time. When animals go to war it is only from necessity, not greed.
An enduring set of traditions, even an atheist would agree.
Yes because, except for a few of your examples, they are not unique to humans at all, they just are not formally practiced in nature, but most are taught by parents to their off-spring over millions of years.
You seem to forget that we are just newcomers to the world, and it is the industrialization and ruination of the ecosystem which will inevitably result in our extinction, but the insects will be the last to go. They know how to survive. We are talking about practical survival techniques, which tend to respect territorial rights such as the wolf's marking their territory to warn trespassers..
p.s. I did a little reading and discovered that Lilith apparently exerted her equality to Adam and when she named the unnamable (is that why you identify God as G-d?), poof she just disappeared but became a demon temptress of men, giving birth to a hundred children each day and thereby spread evil into our previously supposedly "moral " world. She was then replaced by Eve, who also disobeyed her husband Adam, and thus established the tradition that women are inherently evil and should be forbidden to use their wiles to tempt men by guile instead of violence. Actually this was already practiced in nature for a long, long time before men appeared on the scene. Several male ground dwelling birds decorate their ground shelters with gardens of pretty thing to impress the females. Do you agree with that tradition?
Almost all human advancement are a result of observing natural behaviors, such as flight, submarine propulsions, agriculture and husbandry as practice by herder ants. You believe these abilities went unnoticed as humans became more aware of their environment. The first airplanes had flapping wings which immediately crashed because we had no knowledge of the principles of aerodynamic "lift", which problem had been solved ~500 million years ago by , guess.....insects.
We just invented how to cope with natural phenomena by acquiring knowledge of how things work in nature, just like all living things.