As a theologian I do have some comments. First of all the difference between the 3 first you mention is that they are monotheistic ones. Then, Jesus, for the Christians wasn't just a religious leader but supposedly God's Son himself - which is not the case for the rest. There are many details like that which only within research make actually some sense. The point is though, besides studying and all, faith. The most important thing to remember when it comes to religions (and I say this with some certainty after a decade and more studying them) is that sometimes evidence is not as important as faith...
In a lot of the more mystical religions or mystical groups within bigger religions, experience (as a form of evidence) is greater than faith (defined as a blind choice to believe). Faith, as a virtue, is something greater than we commonly think of it. It's something obtained after a divine or mystical experience and not just a mental construct or something you lie to yourself about.
I don't see mystical experience as part of any religion, personally, but I see what you're saying. And of course, what you choose to 'believe' sometimes can be just lying ;)
Understood. There are mystical traditions within the various religions, like Sufism (Islam), Kabbalah (Judaism), Orthodoxy (Christianity). At the deepest core of these traditions is a kind of unification of all religion and therefore mysticism seems to transcend religion. Although religion can provide a gateway to and a structure for the attainment of mystical experience.
As a Greek Orthodox and theologian, may ask what is your field of education? I'm asking this because saying that orthodoxy is a mystical tradition of Christianity is not only extremely offensive but mostly amazingly uneducated on the matter. Unfortunately my time doesn't allow me to elaborate further on that, but that's why there are books (not only the internet), so I would suggest you open one to see that the first Christians back in the day were basically Orthodox. Even the term Eastern Orthodox Church doesn't really apply as because originally, before the Schism, there was only one, the Orthodox one. But saying it's a mystical tradition is beyond me, to the least continue this conversation - I liked at first but now I see there's no common ground of education to go on with it!! I'm so sorry, I hope you understand. Steem on!
I'm really sorry to have offended you. I'm careful always to be respectful of other people's beliefs.
A major component in the practice of Orthodox Christianity is the attainment of Theosis. It is even said that it is the purpose of man. If that is the goal, to participate in the divine nature; to become so much like God that you participate in His nature, and there are practices or rituals to facilitate that goal, then it can be considered a mystical tradition.
It's likely that the term carries some extra baggage for you, being associated with magical practices or polytheism. However mysticism refers to the goal (some sort of union with God, not necessarily complete union as that's likely impossible) and any reference to practices (such as magic) are external to the term.
The way the term is used in your culture or in the groups you surround yourself with, likely devout Orthodox Christians, is different than it is used in my environment. I am deeply devoted to the goal of mysticism (some level of union with God), both through study and practice, and surround myself with such people.
I do agree that Orthodox Christianity has a strong claim for being the "one, holy, catholic, and apostolic church" and even hold that as my opinion. We do not disagree there and by labeling it a mystical tradition I wasn't suggesting it was an offshoot or an outlier in Christianity. In fact I believe it to be the truest branch of Christianity (while not in a way that makes other Christians less Christian) and have considered converting.
Some extra reading that might be helpful:
https://www.ancientfaith.com/specials/eastern_orthodoxy_and_mysticism/orthodoxy_and_mysticism_part_1
http://orthodoxinfo.com/general/lossky_intro.aspx
Edit:
https://en.wikipedia.org/wiki/Mysticism