Is there anything in scripture (or even private revelation to the saints) which says that near the end of the world, the world as a whole will come to accept abortion as morally acceptable?
Nothing specific to abortion, although I wouldn't expect there to be. 2 Timothy 3:1-7 gives us:
Which generally points to people being disobedient, which is probably the closest you'll find. The problem, though, is that people have always been disobedient and rebellious. Before deciding the above fits "today", first try to find a point in history where it wouldn't fit. And indeed, much of this comes down to simply different ethics (meaning: bemoaning people who don't abide the church's edicts) . Moving away from abortion (too divisive to have a constructive discussion), while "modern" values may sometimes seem at odds with Christianity, I for one thinks today's society is heading in a positive direction, not a negative one, with a lot of emphasis on equality and the value of all humans, even (tongue in cheek) those that don't profess and follow Christian beliefs. And even those that do.
Likewise, looking at Luke 21 10-11, 25-26 - we have always been at the mercy of nature. The difference now is that we have much better reporting, measurement and awareness (including awareness of our own harm on the world).
On a more personal note, I don't think obsessing about end of the world prophecy is healthy in a culture. I'd much rather we all got on with living our lives in accordance with our values, and to the greater communal (local and international) good.
So: no, and no.
The idea is based on the following logic:
In Exodus we learn that while Israel resided in Egypt under the oppression of the Pharaoh, God planned to bring a deliverer to His people: Moses. However, when Moses was born, Pharaoh had issued a decree to slay the firstborn sons. Moses was spared from this slaughter by the providence of God, and went on to lead God's people out of Egypt.
In Matthew we learn that Herod sought to prevent the birth of the Christ by slaughtering all male children. Christ was also a Servant of God and a leader to God's people, destined to lead God's elect out of the hand of their enemies.
Some conclude that:
Anyway, take it for what it's worth, but that's the origin.
There is nothing in scripture which makes this statement. As far as private revelation, nothing I know of, however, I do not typically seek out teachings based on private revelation. 2 Peter 1:20-21.