Well, there are a few problems with that theory.
First of all, it's not clear why they would actually have a conspiracy to keep shrooms secret. Using hallucinogens was perfectly legal, and other mystery cults (e.g., the cult of Eleusis) did it too as part of their initiation. And at least one Roman Emperor off the top of my head was initiated too, plus a whole bunch of senators, so it's not like they'd make their own passtime illegal.
While a good case can be made that Paul's Xianity COULD have been a mystery cult -- keeping it for the initiates is the least crazy explanation for why he writes 20-page letters about Jesus, yet fails to mention even a single physical trait, saying, etc, of Jesus or even location associated with Jesus, even when it would have solved whatever he's arguing right there -- I don't think the later church actually conspired to keep anything secret. The more parsimonious explanation is that if you have too few initiates (we really only know of Theudas) and someone else starts a less mysterious sect, with full details of Jesus, it will overtake you. Basically rather than try to keep secret, some guy we now call Mark or the founder of whatever church he was in, went "screw the whole secrets cult and finding excuses when people ask about that guy, let's just MAKE UP a story."
Second, well, I have a hard time taking any theory seriously when it's at the Dan Brown level of ignorance and actually think that that decision was made at Nicaea or by Constantine at all. Sorry.
The truth is actually MUCH sadder, although also less glamorous.
First of all, actually Constantine never drew a canon. The final composition of the Bible wasn't decided until looong after his death. As far as Constantine was concerned, as long as you agreed with a basic creed about Jesus, he didn't give a screw about what gospel you follow or what details you believe in around that creed.
Second, and this is the good news for the religious, the actual texts that went into it were written LONG before Constantine. And the 4 gospels were already chosen by the sect that would become dominant around 180 CE or so, when Irenaeus mentions them. That's like a century and a half before Nicaea or Constantine. Other sects followed other gospels, and even in catholicism there was still debate which epistles are genuine and which should be left out, but the 4 gospels were already canon for the catholics since at least 180 CE.
Third, however, this is kinda funny and what makes the story even sadder. The choice actually seems to be even more arbitrary than people think. At least involving Constantine and a bunch of bishops and all, has SOME legitimacy. There would have been some consultation and voting there. The real version doesn't even have that claim to legitimacy.
If you draw a timeline, pretty much nobody has even heard of the 4 gospels until Irenaeus mentions them. Then suddenly they're all the rage. But previously even when church fathers like Justin Martyr argue with unbelievers and give quotes, they obviously never heard of these 4 gospels, because they'd solve some things right there. But nobody quotes them, somehow. (Apologists produce claims that they have quotes, but they boil down to finding some simple and common sentence in some epistle that also exists in a gospel, and going, "look, he quotes Matthew!" No, he doesn't.)
Note that I'm not saying that they were necessarily WRITTEN in the 2nd century (although they COULD theoretically be). I'm willing to allow that they're WRITTEN by the end of the 1st century. But they don't seem to have much of a following until the late 2nd century. They're at most some obscure texts that haven't yet gained much traction or even popularity.
Then suddenly Irenaeus travels around and manages to get a couple of churches (still very small groups at this point) to form a cartel -- that which we'd later call catholicism -- and wouldn't you know it, suddenly had 4 gospels which are proving THEIR dogma to be true. And a long (and stupid) argumentation for why only these 4 can possibly count, and everyone else's gospels are automatically false.
Now the problem here is that it happens in the middle of a MAJOR Roman persecution of Xians. Irenaeus himself got his post as bishop after his predecessor ticked off the Romans and got himself executed. You wouldn't have large groups of Christians travelling to a big conference to vote on it. That would be a recipe to get themselves all rounded up and executed. It's just Irenaeus and a couple of other bishops that take a fully arbitrary decision.
So, yeah, I see no reason to blame Constantine there. Not just it's unsupportable historically, but even if I were in a mood to lie against Jesus, WTH, the truth is more damning than any lie I could come up with.
Third, the connection to Mithras is very tennuous anyway, because we don't really know what the Mithranists were doing at the time. And we certainly don't have any mention of shrooms in their rituals.
In fact, for what we do know, they didn't need any shrooms to get their believers drowsy and prone to suggestion and confabulation. They actually used cellars without windows, and with a candle or two thrown in for good measure. Pack enough people there for a sermon, and that room's O2 content will drop quite a lot by the end of it. Add the gloomy atmosphere, and the whole mystery theme (including the implication that if you don't toe the line, you'll not get initiated in the next level of the mysteries any time soon), and you have all you need to keep people coming back for more. In that setup, really, shrooms are superfluous.
