Before going deep into the difference between belief & knowledge or discussing issues of ethics and morality, we should first and foremost be able to differentiate between existence and non-existence.
Perception is "King"
With our senses as our only interface between our minds and the external reality, we can quickly realize that perception is "king". Our ability to perceive is the ultimate limiting factor.
For this discussion, we can ignore certain questions about the ultimate nature of reality. Philosophical questions such as: "Are we living in a matrix?" or "What if we are just brains in jars?" could be said to be irrelevant. For one, the limits of our perception would prevent us from ever addressing such questions. Secondly, in either scenario, we would still have this perceived reality to deal with.
Existence and Manifestation
The single defining criteria for differentiating existence from non-existence is manifestation. When something manifest itself (and thus we can preceive that manifestation), we would say that that something exist.
Simply put, something is said to exist if we can preceive of its manifestation.
Manifestations may be directly observable or indirectly observed. For example: light is visually observable directly; solid objects can be directly detected by one or more of our senses; gravity can be observed by observing/measuring its effects on matter, etc.
Objections?
Some may have objections to how existence is defined here.
For example, what about non-manifesting existent objects? Well, it is possible that such objects exist. However, what does it mean to say that such an object "exist"? Firstly, how do you determine that such an object is in existence? If it does not manifest, what criteria are you using to verify its existence? How do we differentiate non-manifesting-existent objects from non-existent-(and therefore, does not manifest) objects? My answer: there is no criteria to differentiate and thus meaningless to say that any non-manifesting entity "exist". In calling such objects "existent", we effectively castrate the word "exist".
What about manifesting objects that we have not had perception (observation) of? This one is simple. That answer would be "we don't know yet". The same criteria applies. If we had not had verifiable observation of the object in question, whatever would it mean to say that it exist?
Acquring knowledge of existence
To correctly acquire knowledge of the existence of entities/effects/etc (therefore, external reality), we must also understand the ability of our senses. We need to realize the limits of perception and how we may be able to improve/support them.
The Scientific Method comes to mind. The methodology of science eliminates error and bias by design. It holds practitioners of science to the highest evidentiary standards - requiring that they produce evidence for their hypothesis that is demonstrable and verifiable with sound and valid arguments. To date, the Scientific Method is the single most reliable method that humanity has to differentiate fact from opinion.
Through science, we have realize the limits of our senses. And has since devised various instruments to assist our senses in our pursuit for knowledge. Instruments such as telescopes, microscopes, spectrometers, spectogram, voltmeters and etc.
We also learnt of the errors our senses are prone of making and how reliable they are. And thus made efforts to rectify or avoid such errors that may arise. For example, we understand that eyewitness accounts, though helpful, is prone to various faults and thus is one of the weaker forms of evidence. Another example would be realizing the importance of collaboration in making observations.
In conclusion...
We can conclude that for factual matters concerning the state of existence, we can reliably utilize the Scientific Method (which is, in a sense, our boosted senses) to detect manifestations to establish the existence of entities or phenomenons.
Given the above discussion, questions about existence is clear cut. If we do not have evidence (that withstands the standards of science) of manifestation, we do not have the "right" to claim existence. In such cases where evidence is lacking, claiming existence is meaningless. It usually demonstrates a lack of integrity or of understanding or even both on the part of the claimant. The correct answer would be "we don't know".
The diametrical answer that claims "X does not exist" in same scenario would also be logically untenable if the claim is absolute. Such a claim in common language would be fine for most intents and purposes. Note that absence of evidence is not evidence of absence.
