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From Buddhist perspective, phenomenal (experiential) reality is dependently co-arisen phenomena. In other words, experience depends on convergence of a number of factors. Some of those factors are common across multiple cases of perception, and some are specific to an individual case of perception. To the extent that some factors are shared, realities are similar. To the extent that some factors are unique, realities are dissimilar.
This topic is discussed in depth in a very advanced work of 19th century Buddhist philosopher Mipham, called Beacon of Certainty (topic #6). For a more casual read, check out The Prayer of Kuntuzangpo. Also see Lamp of Mahamudra section one, "Ground Mahamudra".
P.S.
The objects (and subjects!) appearing in each of the realities are not truly existing. But there is only one ground underlying them all. To realize the true meaning of this ground is to be Buddha.
There is an infinite number of valid, internally not inconsistent, but not necessarily compatible with each other, ways to cognize this ground. Although all cognitions (including cognition of the true meaning of the ground!) are construed on the basis of temporarily combined elements (so in this sense no one cognition is fundamentally better than any other), however, since there's a case of being aware (vs. being unaware) of dependently-coarisen nature of objects (and subjects!) of perception, there's a sense in which we can speak of an awakened cognition. Or as Master Dogen said in Genjo-Koan:
When all dharmas are [seen as] the Buddha-Dharma, then there is delusion and realization, there is practice, there is life and there is death, there are buddhas and there are ordinary beings. When the myriad dharmas are each not of the self, there is no delusion and no realization, no buddhas and no ordinary beings, no life and no death.
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Reality is neither consensual or an individual perception. Of course when one practices Vipassana and realize what reality actually is, then your individual perception of reality coincides with the actual reality. Until then there is a divergence. Practice of Vipassana is to close this divergence where you move from gross reality to the subtlest realities until you have realized the ultimate reality. Also if we see reality as it is then your would be enlightened or as an individual an Arahath, which is achieved through Vipassana. As many individuals are not enlightened their perception of reality in different from the actual. Also note, consensus view on any things is cultural and time wearying and definitely will not coincide with reality. Even science is in a flux of change with new theories and old being dispelled. So scientific understanding is not reality per say through it is and approximation of reality.
E.g. When you play doctor in kindergarten then you are not a doctor but when you actually become one then this is the reality. Many are in the kindergarten stage of understanding of reality but have not progressed. Similar to a person not going to school. Once you learn and then go to medical school then you only become a proper doctor. Similarly when you practice Vipassana only you progress to higher stages of understanding of reality.
Also see: Reality in Buddhism
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What is the "reality" in your question?
Are you asking about Sacca,
Sacca (Pāli; Sanskrit Satya) word meaning "real" or "true".[1] In early Buddhist literature, sacca is often found in the context of the "Four Noble Truths", a crystallization of Buddhist wisdom. In addition, sacca is one of the ten pāramitās or "perfections" a bodhisatta must develop in order to become a Buddha.
In the context of the "four noble truths" I guess Buddhists see (that kind of description of) "reality" as "applicable to everyone" or "general".
Pāramitā suggests that insight (into reality) and ability to speak truth (about reality) is Buddhist: i.e. it is something which the Buddha can do.
This may be another question-and-answer about that topic (i.e. "sacca" or "satya") here: What is Sat-Dharma?
If you're asking about "physical reality" then I don't think so -- I think that Buddhism describes a reality that's more complicated than merely 'physical' reality.
If you're asking about conscious or experiential realities then, well, I won't try to answer that. Maybe that's getting into material in the Abhidhamma.
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In the early suttas, this sort of question is deemed irrelevant for the practice; that is, as long as there's a problem, and you can do something about it, then any time wasted on wondering whose problem is it, what constitutes a problem, does it have an inherent existence shared by all beings, etc, is categorized as falling victim to Mara. [1]
That being said, here are a few things to consider: