No. Not true at all, on almost every point above. Not even most fundamentalists believe that everyone has to believe everything exactly the same ways. The only groups I've ever seen that demand everything think identically on all matters of faith are authoritarian led cults which are way out there on the fringes, typically dangerous and unhealthy groups which drink the kool-aid when dear leader goes over the edge because they have given over all control of independent thoughts to them.
From such an extreme at one end there is a wide spectrum of views away from that point which can be called Christian faith. Being united in faith, is not the same thing as being of one "belief", which is how you put it above. There is a difference between faith and belief. Beliefs are ideas of the mind. Faith is a confidence of the heart, or a gut feeling. Beliefs are mental in nature. Faith is visceral in nature. Different, albeight interrelated and interconnected domains.
So first from above, "the one true religion". Not all Christians imagine Christianity as exclusive in that way, that unless someone converts to the religion and adopts Christian symbols and rites, that they are lost on on their way to hell. Certainly there are those who do believe that. And there are those who do not believe that. A "true religion" really means an authentic religion that brings about authentic, genuine spiritual transformation through its teachings and practices.
There can in fact be many true religions in this sense. Not just one to the exclusion of others. It is not seen as "If this is true, than everything else has to be false", mentality. That's binary black and white thinking. It is 'either/or' thinking. But there is the more realistic and rational understanding of a 'both/and' mentality, which sees that truth is not exclusive, but inclusive.
"Many paths lead from the foot of the mountain, but at its peak we all gaze at the single bright moon", said the Zen poet. That reflects my view on these things.
Now, as far as the "unifying power of the Holy Spirit", I would agree that is the factor that can and does unite disparate views and personalities, and cutures, and beliefs. But NOT at all in the sense of a common ideaology or belief system. The exact opposite of that. There is a massive difference between uniformity and unity. Unity requires diversity. Sameness of ideas and views creates weakness. It's all the grains running the same direction. Whereas a woven material of criss-crossing patterns is far more strong. That unity is LOVE, not beliefs.
In this sense, it is the mystical heart of all religions, that unifies them in a common connection. It is a spiritual unity, of the heart, of the soul, not of our ideas about things that is considered the "Spirit". Unitive Consciousness, is another way to think about that. It's our connection of the heart that unites, not our agreement of our ideas.
And this too is a view that is found not only in Christianity, but also all religions at the deeper realization of the nature of what a "true religion" is about. Which is the mystical heart of faith itself, which transcends religions.