Starting at the end of your post:
We differentiate between facts and feelings because that differentiation is relevant enough for us to discuss them as separate from each other.
Of course. It seems reasonable to assume that the only reason humans differentiate between any two concepts is because that act of differentiating serves some purpose.
The fact that the planet Mars appears of a red hue obviously seems of quite a different order from my desire to paint the ceiling red. But in the sense that facts are considered relevant for managing our way through life, I might be far more concerned with my feelings about interior décor than about a pin-prick of light in the night sky. Both are, in any case, real in the sense that they are parts of my reality. Just because one enjoys universal consensus does not make it any more real than the other.
What I would ask you to consider is the idea that we live in a culture in which the objective fact is promoted for political ends (the regimentation of society) as some sort of ultimate truth, whilst the subjective facts of one’s feelings are systematically downplayed (for the same political reasons) — except when they can be exploited for commercial gain. Hence we see marketing targets all sorts of personally indulgent behaviour ‘because you are worth it’ etc. that panders to subjective feelings, whilst the main institutions of our societies (academia, the media, government bodies etc.) emphasise a supposed need for objectivity. The underlying political goals can distort the individual’s view of what is relevant and how important our different forms of knowledge really are.
Speaking in very general terms, when the sway of the church began to collapse, political control had to be rethought, and so it attached itself to the successor of religion which was the scientific and objective view of reality… a view in which, just as was done through the church, the citizen’s view of the world could be manipulated. Hence we have all sorts of pseudo sciences such as economics and social sciences that always downplay anything subjective, whilst psychologists dictate what is to be considered madness — usually nothing more than whatever behaviours are not socially normalised. In the passing it also became necessary to exaggerate the deterministic view of reality in order that a new form of authoritarian religion — formalised science — could be propagated. We are living in the midst of the results, and our cultures are drenched in the dogma of scientific progress — even when the results of this outlook threaten our very existence by ruining the planet’s biosphere.
People quickly defend objectivity and the status quo with comments like You can’t just run society on one person’s whims. But if you stand back and look at societies, they are in any case run by powerful elites — not by scientific objectivity. Arguably it is actually the subjective feelings of individuals that are calling the shots — e.g. Trump and his ilk.
Other than that it serves political goals, the obsession with objectivity, IMHO, only stems from the desire to exploit our environment as part of the religion of science and, although poorly recognised, to exploit one another.
From this angle, science and the fact-based model of objectivity have blossomed because they are expedient. But expediency does not necessarily reflect any true understanding of the world. And when we see that our exploitation of the material world is proving increasingly problematic in terms of the damage to our only life-support system (Earth), the suggestion is that we actually do not understand much in the manner we imagine we do. You can think of this as setting your house on fire to keep you warm. If you do not understand what you are doing and the likely consequences, you have the desired result of being warm - that is, until you have to deal with the consequences of failing to see the weaknesses in your model of what you were about. This is the stage humanity is at. In general, it thinks facts are sacrosanct and constitute a sound understanding of reality. But the state of the planet is increasingly telling us that using our limited forms of intelligence to exploit our environment, as if whatever aspects of reality remain missing within those forms of intelligence were of no consequence, is a form of stupidity.
As regards facts and feelings, the semantics of any concepts can be pulled apart ad infinitum. That does not achieve much. But there are good reasons to be actively suspect of something purely by virtue of it being deemed a fact. Being a fact tends to be taken as indicating that something is established and therefore does not need any further questioning. But within an inherently mysterious universe, a fact is just an idea that proves repeatedly useful within an incomplete and possibly incorrect idea of how that universe works. Paying attention to personal feelings can prove more useful, and is arguably what really helps us understand the human condition. Bear in mind that animals apparently do not deal with anything equivalent to our formalised facts, and yet they do just fine by using their senses and feelings. The ‘fact is’ that feelings are arguably more important in understanding the behaviour of life forms than facts are. Thirst, hunger and all other essential survival instincts are realised as feelings — it is only the mind that optionally formulates them as facts.