I think, like every other proposed utopia to date, any such system would 1) be horrible to live under, since it's would need to be a near-totalitarian system ruling over a large, non-homogeneous population nonconsensually, and 2) fall apart in five minutes through in-fighting, since no one actually has the ability to control what billions of people think and believe and do.

Also, your question depends heavily on drawing a boundary between culture and ideology that I suspect is fuzzier in practice than that. Suppose you succeed in unifying every human, and we all agree to live by a single set of ideals. What happens next? We have to figure out how to apply them, and how to resolve disagreements about how to apply them, because any ideals worth living by are complicated, and humans are not logically omniscient. We have to teach the next generation those ideals, and persuade or coerce them to live by them. Even if you define your system with mathematical precision, and go full Shining Garden, average humans will just be abiding by the output of a decision-making process they can't independently reproduce, and (after a while) much of which happened before they were born - aka culture.

Side note: the use of passive voice in your question is a big red flag for me. Who does the removing? 

Similarly, "the system of opposing beliefs" sidesteps the whole problem that (like Moloch), it isn't so much a system, no one instantiated it, it's just a consequence of us all being able to think and learn and not leading identical lives or having identical drives, wants, and needs.

Still, my answer is: trivially yes, that scenario would result in unification, but by default I would be extremely strongly opposed to any path that led in that direction, and would need a heck of a lot of convincing to even consider any proposal of that sort.