It's very bad. To address some points of the argument, mostly focusing on the bits about ancient cults and Eleusinian initiation:
According to Muraresku, initiation at Eleusis consisted of drinking 'an unusual elixir', followed by a 'beatific vision', and going home in the morning. Every word of this is false.
Initiation wasn't 'one night at Eleusis', it was a long complicated procedure that took a week and a half. The 'unusual elixir' wasn't the climax or anything, it was just one stage in the proceedings.
The elixir wasn't 'unusual'. A kykeon was a generic term for a refreshing barley drink. It's attested mostly in medicinal contexts, to perk up sick people, but a couple of ancient sources are clear that it could be used for people who were tired and needed an energy boost. The day of fasting that preceded the kykeon at Eleusis is plenty of motivation to explain why an energy boost would be needed. There's no evidence of any mind-altering substances in any kykeon at any date, with one exception in Homer's Odyssey where the witch Circe explicitly adds magical ingredients to a kykeon.
The 'beatific vision' was invented practically out of thin air by Carl Kerényi in 1960. It isn't in any ancient source, unless you mistranslate and wilfully misinterpret the context -- which is exactly what Kerényi did, misinterpreting references to the deiknumena or sacred objects shown to Eleusinian initiates as references to '“ineffable” and “holy” “Phantoms”’ (1967: 99; the three words come from three separate ancient sources!). Muraresku doesn't provide any additional support for a 'beatific vision', and isn't even aware that it was Kerényi who applied the phrase to Eleusis. In fact Kerényi's phrase was the Latin visio beatifica, which should already arouse suspicions since it's obviously not Greek: in fact the phrase originated in a 14th century Catholic religious controversy about whether or not good people get to go to heaven before the Second Coming. It didn't have anything to do with mystical experiences, and there's nothing to suggest any mystical experiences at Eleusis, beyond initiates finding the whole week-and-a-half process very memorable and symbolic.
Pause here to re-emphasise that Kerényi's phrase 'beatific vision' is literally the entire basis for every piece of Muraresku's argument. The fundamental premise of the book is a fabrication.
Muraresku routinely cherry-picks his evidence without looking at it. Take a look at the chapters on Eleusis and see if you can find what the ancient documentary sources actually say about a 'beatific vision'. The one salient source that Muraresku cites, a bit of Plato, he attributes to the wrong work by Plato. If you go and read the ancient sources he cites, you will have done more than he did. Let's carry on now.
Muraresku's parallels for mind-altering mixtures at ancient cult sites are in Catalonia and Israel, not anywhere in the Greek world; they don't involve Greek divinities; they have nothing to do with the cult of Demeter, Kore, or Hades; there's no evidence to suggest that the presence of potentially mind-altering substances was intentional (ergotised barley occurs naturally, and juniper use doesn't normally have anything to do with getting high); they're explicitly alcoholic mixtures, and the kykeon at Eleusis is explicitly non-alcoholic; and we have no documentary evidence of any kind for any use of mind-altering substances, in any Greek cult, except alcohol.
Ergot is not LSD. Ergot is toxic. It can in rare cases be psychoactive, but more often it's going to cause vomiting or diarrhoea. If you use it regularly, it causes gangrene. Don't consume ergot.
Ergot can be turned into LSD ... if you have an advanced knowledge of chemistry and you have access to chemicals like diethylamine and pure hydrazine. (Pure hydrazine tends to explode when exposed to air, by the way. Remember the scene in The Martian where Mark Watney is trying to turn rocket fuel into water and it nearly blows up his habitat? That's hydrazine.)
The book suffers from specious argumentation and tendentiousness. Muraresku’s strategy is a classic case of the Gish Gallop. He repeatedly brings up sources and real archaeology; then he asks leading questions, so as to generate a speculative ‘maybe’; then he treats that as 'there is evidence' for the rest of the book. He always presents evidence as unambiguous: no inconvenient exceptions, no weighing up of competing interpretations. I mentioned already how evidence for a juniper-wine draught at Tel Kabri in Israel, or a nightshade-wine draught in Dioscorides, become evidence for LSD in a non-alcoholic drink at Eleusis. He does this constantly.
As for the tendentiousness, ulterior motives are obvious throughout. The book is intensely ethnocentric: Muraresku's interest in antiquity seems to stem from seeing modern America as the heir to 'Western civilization' (a phrase that he uses a LOT), as if 'civilisation' is a piece of property that one person owns at any time. At one point he even refers to 'things our Greek ancestors and Founding Fathers worked so very hard to establish. Purposeful things like law and order, common sense, and clean living ...' I find his approach to the history of Christianity very much in the same vein, though I'm not as well equipped to dissect it: things like casting the Vatican as involved in a vast conspiracy to conceal the truth because it publishes indices to its archives in Italian, or because you have to travel across Rome to get to them (the horror!), is obviously tendentious.
Enough said. The book is full of spurious thinking, based on false premises.
Edit: failed to end a sentence.
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