I know that Hofmann and a handful of historians theorized that, but what is the evidence?
For Hofmann and his collaborators the evidence lay in two points:
Hofmann speculated (without any evidence) that the wheat barley was infected with ergot, which is hallucinogenic. The rest of the study was based on juxtaposing cherry-picked facts that may or may not be related (e.g. the practice of adding herbs to wine in non-ritual contexts) and selective interpretations of evidence (e.g. if Plutarch refers to wine as a pharmakos, that means it's psychoactive for some reason other than the alcoholic content).
(Just to be clear, the kykeon did not contain wine and the Hymn to Demeter opposes it, as a ritual drink, to wine, a non-ritual drink.)
So the basic argument boils down to point 1: the idea is that having a religious experience implies hallucinogens. That certainly does not follow, and that's why the study has never really been taken seriously, barring a couple of exceptions. The presentation of the data in their book The Road to Eleusis sounds nice and professional, but if you look at the actual argumentation, it's all cast in speculative terms. E.g. p. 63:
...the hierophants may well have withheld from them the Secret of Secrets... May they not have discovered a kind of ergot that contains solely the hallucinogenic alkaloids such as has been found in modern times in ergot of Paspalum distichum? Indeed herbalists other than the hierophantic families may have shared in this discovery...
One of the exceptions may be worth mentioning, though: in 1978 the famous linguist Calvert Watkins published a linguistic study of the word kykeon and words for various grains, in which he thought he had found Indo-European origins for a hallucinogenic kykeon, taking Hofmann as his lead. However, if you look past the masses of linguistic details in his paper, he only thought there was a hallucinogenic effect because of the pennyroyal in the kykeon. But pennyroyal isn't a hallucinogen: in the argument of Hofmann et al., the hypothetical ergot was the key ingredient. Pennyroyal was a standard cooking ingredient in antiquity, in totally non-ritual contexts. Its main medicinal effect is as an abortifacient.
Given how much credulity The Road to Eleusis has received outside the field, it's a shame there's never been a detailed review of the trivia cited in Ruck's "Documentation" chapter, because it does look professional, and glancing through it I can see how it could be persuasive; but it's really just a collection of material on unrelated or barely-related topics, combined with speculation. The closest we get is a brief report by Walcot in Greece & Rome 26 (1979), p. 104:
As perverse as it is unconvincing will be the verdict of many of those perusing The Road to Eleusis... Carl A. P. Ruck argues that barley, or rather ergot of barley, was 'the likely psychotropic ingredient in the Eleusinian potion' (p. 47). Much of Ruck's evidence is dubious: thus at once point we are said to hear of wines so strong that they could be diluted with twenty parts of water (p. 41); no reference is given but one thinks immediately of the wine given Polyphemus by Odysseus, and that this is Ruck's evidence is confirmed later (pp. 89-90). And what does this prove apart from Homer's fondness for heroic exaggeration? Somehow or other Ruck makes everything conform to 'an herbal context', perverting in the process the interpretation of any number of Greek myths. There are also some quite fantastic etymologies, e.g. Iasion, 'the man of the drug'; Mycenae, of course, is linked to mykes (p. 119), which suggests the mushroom featured in Mycenaean religion. Everything is wildly out of hand, and it does seem hard when the argument of another scholar is rejected as 'extraordinarily biased' (p. 123), especially when that scholar is Mylonas.
Edit. If you want a better idea of what the experience of initiation looked like, obviously the evidence is very sparse. But what evidence there is points not to hallucinations, but more towards a vigil combined with theological revelations about the allegories underlying the foundation myths. That is, the hierophants were probably more theologians than drug-dealers. Think of them as the scientologists of ancient Greece. Here's a passage from a 2008 paper by Fritz Graf that I find quite suggestive:
[Synesius] juxtaposes two groups of extraordinary men who open up to divine inspiration: the very few who have an immediate access to the divine, such as Egyptian ascetic monks, and the many religiously minded who need rational arguments to be brought to the jumping-off point of revelation. Bacchic mysteries are a reference point throughout this discussion. Synesius refers to Plato’s quotation of the famous verse of Orpheus, πολλοὶ μὲν ναρθηκοφόροι, παῦροι δὲ τε βάκχοι: "for there are many that carry the thyrsus, but few are the Bacchi": this Bacchic and Platonic dichotomy reflects the two ways of attaining inspiration. ... The dichotomy goes back to Plato himself, although Plato used it differently, to describe the process of philosophical acces[s] to truth in mystery language.