But in Catholic and Orthodox Christianity, belief is central to the rules and rituals.
In every Catholic mass, the congregation "proclaims the mystery of faith" and "professes their faith": they're ritualized, yes, but they're statements of belief. In the ritual of the Eucharist, the priest gives - effectively - a running commentary of what the Church considers to be the factual basis for the different parts of the ritual.
Yes, there are practices and rituals - boatloads of them - but there's just as much belief and factual claims.
Yes, but the practices and rituals are what are beneficial.
People can either believe in god or not believe in god, yet as long as they follow the practices and rituals they benefit. The believer does not gain from a supernatural reward post-death, they gain as the practices bring tangible benefits in the real world.
If they only believe in god without following the practices, then they do not. The non-believer who practices gains more than the believer who does not.
If the benefit comes from the practical aspects, not the belief aspects, then belief is ultimately irrelevant. Religions are products of human experience, through experience we learn things that work and things that do not. If religion 'didn't work', it wouldn't still exist all over the world. We don't have to be able to create a 'rational' justification for everything that comes along with it, just accept that the balance of probabilities says if it's survived this long, there must be some tangible benefits that come along with it.
The person in this thread most familiar with Buddhism has said that the practices of Buddhism would be pointless without the factual claims being true. If you have other Buddhist perspectives to share, I'm all ears.
That would suggest that the practices themselves have no tangible benefits outside the objective truth of the totality of the message.
I'm not saying that you can ignore the teachings as they relate to the practice, just that the metaphysical justifications behind such teaching do not need to be true.
If you rejected any idea of rebirth and thought that there was only one life, you can still benefit from practicing Buddhist rituals. Much religious teaching is about finding an inner peace/freedom, and many give you practical steps towards doing so.
What matters is that you accept that following the rituals and practices brings you benefit, not that you come to the conclusion that they express singular objective truth. The benefit comes from belief in the ritual, rather than belief in any metaphysical justification for the ritual. You don't have to believe that the Buddha was born miraculously or reached a state of pure enlightenment or believe in reincarnation, just that the practices bring you benefits if you follow them properly.
That is why many religions have similar rituals, but different justifications behind them. Fasting forms part of countless belief systems, yet they all use different justifications for it. If 10 people fast for 24 hours, but all based on different religious teachings, they all benefit equally from the practice regardless of the specific reasons justifying the action.
The justification doesn't matter, only the proper practice.
