"Flux", a novelette by Barrington J. Bayley and Michael Moorcock, also the answer to this old question and this one; first published in New Worlds Science Fiction #132, July 1963, available at the Internet Archive.
1. I read it in an anthology during the 80's. The anthology may have been older than that.
Perhaps Voyagers in Time, an anthology edited by Robert Silverberg.
2. Narrator is sent by an organization to view the future. He does this on multiple occasions, with the future becoming stranger each time. I'm not sure of the method used to grant him this view.
Max File, the third-person protagonist (not narrator), is sent in a time machine by the European Economic Community to view the future. However, he is only sent once; he gets lost in time, and views many strange time-worlds while trying to find his way back. He gets his instructions:
"Our only hope lies in discovering how events are organized in time—this might sound highly speculative for such a serious and practical matter, but this is what things have come to. In order to take effective action in the present, we must first know the future. This is the mission we have in mind for you. The Research Complex at Geneva has found a way to deposit a man some years in the future and bring him back. You will be sent ten years forward to find out what will happen and how it will come about. You will then return, report your findings to us, and we will use this information to guide our actions, and also—scientifically—to analyze the laws governing the sequence of time. This is how we hope to formulate a method of human government for use by future ages, and, perhaps, remove the random element from human affairs."
3. His perspective of observation is quasi-orbital. He views Earth from a great height and can zoom in for greater detail.
Mostly, the time machine remains on the ground, but you may be thinking of this part:
File looked at the date register. It told him he was now fifteen years away from Appeltoft, anxiously awaiting his return to the Geneva Complex.
He tried again.
A lush world of lustrous vegetation swayed and rustled in a hot breeze. A troup of armadillolike animals, but the size of horses, paraded through the clearing where File's machine had come to rest. Without pausing, the leader swung its head to give him a docile, supercilious inspection, then turned to grunt something to the followers. They also gave him a cursory glance and then they had passed through a screen of wavy grass-trees. He heard their motions through the forest for some distance.
Barren rock. The sky hung with traceries of what were obviously dust clouds. Here the ground was clean of even the slightest trace of dust, but a strong cold wind blew. Presumably it swept the dust into the atmosphere and prevented it from precipitating, scouring the rock to a sparkling, ragged surface. He could hardly believe that this scrubbed shining landscape was actually the surface of a planet. It was like an exhibit.
Now he was in space, protected by some field the time machine seemed to create around itself. Something huge as Jupiter hung where earth should have been.
Space again. A scarlet sun pouring bloody light over him. On his left, a tiny, vivid star, like a burning magnesium flare, lanced at his eyes. An impossible three-planet triune rotated majestically above him, with no more distance between them than from the Earth to the Moon.
He looked at the date register again. Twenty-odd years from departure.
4. He is mainly engaged in observing continental Europe. During one of his observations, he determines that the majority of the European public now belongs to single-sex organizations that are at war with each other (Male vs. Female).
This is at his first stop:
As he mounted an interlevel ramp he saw one or two figures, mostly alone. He had never seen so few people. Perhaps the quickest way to find out what was going on would be to locate the library and read up some recent history. It might give a clue, anyway.
He reached the building which pushed up through several layers of deserted street. A huge black sign hung over the main entrance. It said:
Puzzled, File entered the cool half-light and approached the wary young man at the Inquiry desk.
"Excuse me," he said, and jumped as the man produced a squat gun from under the counter and leveled it at him.
"What do you want?"
"I've come to consult recent texts dealing with the development of Europe in the last ten years," File said.
The young man grinned with his thin lips. The gun held steady, he said, "Development?"
"I'm a serious student—all I want to do is look up some information."
The young man put away the gun and with one hand pressed the buttons of an index system. He took two cards out and handed them to File.
"Fifth floor, room 543. Here's the key. Lock the door behind you. Last week a gang of women broke through the barricades and tried to burn us down. They like their meat pre-cooked, eh?"
File frowned at him but said nothing. He went to the elevator. The young man called, "For a student you don't know much about this library. That elevator hasn't worked for four years. The women control all the main power sources these days."
In the library he reads up on recent history:
—Civil war imminent, the Council temporarily averted by promising that thorough research would be made into every claim for a solution to the problem of over-compression. This, as we know now, was a stonewalling action since they later admitted they had been incapable of predicting the outcome of any trend. The faction, one of the most powerful headed by the late Stefan Untermeyer, demanded that they be allowed to conduct a controlled experiment.
—Unable to wait any longer, the Council reluctantly agreed, and a large part of Bavaria was set aside so that the plan of the Untermeyer faction could be implemented. The plan necessitated sexual segregation. Men and women were separated and each given an intensive psychoconditioning to hate the opposite sex. Next, acts were passed making contact with the opposite sex punishable by death. This act had to be enforced frequently, although not as frequently as originally had been thought. Ironically, Untermeyer was one of the first to be punished under the act.
—It is difficult these days, to make a clear assessment of the results of this experiment (which so quickly got out of hand and resulted in the literal war between the sexes, which now exists with cannibalism so prevalent, each sex regarding it as lawful to eat a member of the other) but it is obvious that measures for reassimilation have so far met with little success and that, since this creed has now spread through Germany, Scandinavia and elsewhere, an incredible depletion of life in Northern Europe is likely. In the long run, of course, repopulation will result as the roving hordes from France and Spain press northward. Europe, having collapsed is ready for conquest, and when the squabblings of America and the United East are ended, either by bloodshed or peaceful negotiation, Europe's only salvation may be in coming under the sway of one of those powers. However, as we know, both these powers have similar problems to those of Europe in its last days of sanity.