Mordecai Kaplan would be unhappy to hear that commitment to ritual and tradition requires belief
I think the issue is not whether commitment to ritual -- as in, a commitment to go through the motions -- requires belief, it's whether experiencing ritual as beautiful requires belief. I think it's plausible that immersing oneself in the context of the ritual, including the requisite belief set, makes it far more meaningful and awe-inspiring. Merely aesthetic appreciation of ritual may not inspire the same depth of feeling as you would experience if every move in the ritual were wrought with spiritual significance for you.
So participating in the tradition without believing may also count as "depriving oneself of beauty". I wouldn't really know, though. I've been a non-believer my entire intellectually aware life, so I have no basis for comparison. I will say that I can't imagine any ritual or tradition driving me into the kind of frenzy you see at some charismatic Pentecostal churches, for instance. But I can't really imagine being driven to the kind of frenzy you see in the average audience for the The Price is Right either, so this may be an issue of personality rather than belief.
Yes, participating in a ritual without believing in it tends to make it feel less beautiful.
Just came across this interview with Robert Aumann. On pgs. 20-27 he describes why and how he believes in Orthodox Judaism. I don't really understand what he's saying. Key quote (I think):
Anybody have a clue what he means by all this? Do you think this is a valid way of looking at the world and/or religion? If not, how confident are you in your assertion? If you are very confident, on what basis do you think you have greatly out-thought Robert Aumann?
Please read the source (all 7 pages I referenced, rather than just the above quote), and think about it carefully before you answer. Robert Aumann is an absolutely brilliant man, a confirmed Bayesian, author of Aumann's Agreement Theorem, Nobel Prize winner, and founder / head of Hebrew University's Center for the Study of Rationality. Please don't strawman his arguments or simply dismiss them!