Part of the idea of "mystery cult" is that there are certain important aspects of the world and the human spirit that
don't go into words. In a sense orthodox Christianity is just such a mystery religion; important things are called "mysteries." (Well, they are if you are raised Roman Catholic anyway, as I was, I've never participated in other denominations, but I do believe many of them preserve the same language and attitude).
When I was in first grade the nun who taught my class in Catholic school told us a story about IIRC St. Anthony; he was wandering on a beach, pondering the deep doctrines of the Church, when he encountered a small boy with a bucket and scoop. The boy was putting more sea water into the bucket which was already overflowing; the man asked him, "what are you doing?"
The boy said, "Oh, I'm going to bring the ocean home in this bucket."
The man smiled and said, "But child, your bucket is already full, look at the vastness of the sea before you, how can you dream of doing such a thing?"
And the boy looked up into the eyes of Anthony and said "And how can you hope to fathom the infinite mind of God with your frail human soul?" and then vanished...
Sister made sure to explain to us six year olds that the boy was an angel sent by God to teach the future saint a lesson in humility.
To be sure, within Christianity there are divisions; some branches were more like "mystery cults" than others--the essential thing about a proper "mystery cult" is that they make some kind of effort to convey that which cannot be conveyed by words by other means--by rituals, by dance, by music, very commonly by drugs integrated into all this. The Initiates who have participated in the Mysteries have indeed learned something new (well, they believe so anyway) but no matter how eloquent and poetic they are, they can't put it into words, because the Universe is not made of words. The orthodox branches of Christianity, following the doctrines approved by Emperor Constantine as part of the process of promoting Christianity to the official religion of the Empire, tend to deemphasize this as much as possible and get quite wordy in their exposition of the nature of God and the duties of a good Christian. Still the whole idea of the Holy Spirit, canonized as an aspect of God Himself, seems to me to be to acknowledge this deeper, preverbal reality, as does a lot of other Catholic stuff I'm familiar with.
Now, if modern Roman Catholicism were in fact a Mystery Religion in the sense that the Eleusian Mysteries probably were, I'd at some point have gone through some ritual or other that would have transformed my consciousness or perceptions at least briefly; perhaps it's because I was some kind of wicked sinner (though I didn't think I was, maybe that was the problem

) but none of the Sacraments ever had that kind of effect on me. I made a big effort to be a holier person after I was Confirmed, and to push past my quotidian concept of reality to grasp a glimpse of something otherworldly during various prayers, meditations, and so forth, but nothing remarkable ever happened. Yet the literature of thousands of years of Christian (and Sufi, and lots of other traditions) mystics is abundant. Later as an adult (legally speaking anyway, dunno if I really qualify as one even yet!

) I did indeed have some fairly mystical experiences using means not actually sanctioned by the Church in my knowledge anyway, and one time just contemplating something (an exhibit of the images stored on the Voyager probe records, at JPL, as it happens). Scholars sometimes call it "the Oceanic Experience" or some such. (Shades of St. Anthony and the angel-boy!)
Another possibility regarding me and my evaporated faith is, I didn't go the full monty--Catholic tradition is full of very stringent rituals of privation, of fasting and self-mortification and so on. Perhaps a monk, or a person on a long retreat, who goes through the physically demanding path prescribed for hermits and the like does indeed come upon something transcendental; a skeptic could say they were simply hallucinating from hunger, thirst, or exhaustion, but the same could be said about many other traditions of "enlightenment" of course. If the blinding insight one comes upon cannot be verbalized, it cannot be placed on a table to be inspected and certified whether it's cosmic truth or just the result of brain electrolytes getting out of balance. The point here is, Christianity has in its deep traditions just such extreme rituals, and they may indeed have been, for the prophets, hermits, monks and other mystics who recorded their findings as best they could just of the same kind of character as the Classical era "Mystery cults."
My guess is that most of the religions you've been lumping in as "Mystery Cults" weren't that--I don't think Mithraism was for instance. Whereas the real Mystery Cults involved some sort of "consciousness-raising," more or less psychedelic experience that, when completed, was simply not amenable to being written down. For such a cult to continue to convey its teachings, if such we can call them, from that day to this, it would have to have continued its practice, making new Initiates and having them in turn initiate others, through the centuries, and you would then have to go to them and be Initiated in your turn to know what they are teaching--and then you couldn't write it down either.
As part of the "spin the wheel and take your pick" approach carlton_bach mentioned above, you might imagine such a cult has indeed survived. But you'd be on thin ice there regarding Board policy, as I understand it--skating dangerously close to "Hidden History" and "conspiracy theory." I can imagine such a cult existing innocuously and thus avoiding the charge of conspiracy--from one direction. You'd still have to explain how it survives a couple thousand years of zealous persecution of the unorthodox by the inquisitions and jihads of various powerful orthodox religions; any explanation involving secret agreements of tolerance risk one kind of conspiracy theory charge and any about them being so clever they never get caught--another. By definition such a cult would be Hidden History...