If I understand correctly, your meaning of religion involves the development of social hierarchies and ruling elites.

Basically. For me religion = institutionalized worldview.

I don’t get is why this particular set of events is the criteria for the advent of religion. It seems arbitrary to me.

I guess, it was not the most fortunate way to arrange that timeline. Not exactly excellent, but better arranged (and simplified), it would look like this:

animism -> shamanic animism -> non-duality -> secular philosophy
           -> polytheism       -> monotheism  ->scientism  

So you’ve referred to the spirit (spirituality?) and polytheism (a pantheon of gods?) in animistic societies.

Spirit is just an arbitrary English word for a concept that in western society has already a totally different connotation. Thus, animistic societies may appear to us as polytheistic but in reality they are not. The plethora of spirits and incorporeal (and other) agents are the same part of the world as humans, animals, rocks, etc. They are not a separate pantheon that gets some special treatment as is the case with polytheistic religions.

Did you mean to say animism is (becomes) a polytheistic religion?

Animism turns, or is transformed, into (i.e. becomes) polytheistic religion.

why do you believe that jimson weed and peyote were not used by the Yaqui/Toltecs for thousands of years prior to the European invasions? Remind me why the Yanomamo don’t count.

I never said that. But they count as shamanic animism (see below for why they are linked with entheogens). The original animism IMO looked more like those societies I have mentioned. After all, it’s obvious that human beings don’t have to use hallucinogens to be able to have visions (or dreamlike worldview). When we are kids we are all pretty capable of that feat.

why a priest is religious, but a shaman is not

Shaman is merely the first “labor specialization” (if we omit the division of labor between male and female). As it seems first shamans were physically disabled individuals, who were probably high due to medicine they were taking to alleviate the pain and discomfort coming with their predicament. But yes, this is merely my interpretation of archaeological data. Another factor is that only priests (when that caste was established) were responsible for redistribution of food.

Why are ceremonial rituals religious but not communal rituals?

Exactly why handshake or a birthday party are not religious rituals. Or are they?