World War III failed to happen in 1958. That event was important to Poul Anderson’s Psychotechnic League future history.
After the Soviet Union broke up, there were still new books about the USSR invading the US. And there were sf writers whose series and/or future histories had the Soviets as one of two superpowers well into the future. Jack Chalker had an easy solution for his Well of Souls series — Nathan Brazil pushed the universe’s reset button. Other writers became rather less explicit about history, or declared their failed futures to be alternate history.
Lesson One: Be prepared to abandon your lovely future.
Lesson Two: If you want to continue using the same future, be vague as possible about what will last beyond this week.
Or you can decide not to care. Use the same future everyone else writing future-set fiction does: aircars will completely replace ground cars, videophones will rule, etc. Modify to the taste of a particular editor (North America becomes Arabic-speaking, the Middle East turns Southern Baptist, whatever.)
But suppose you want to get the future right, as much as possible. There are ways to do it.
Learn what predictions have consistently been wrong: Ground cars were supposed to be completely gone shortly after WW II. (Probably earlier, actually.) Voice-only phones were to be extinct by 2000 CE. (Yes, we have videophones — but they’re not the only phones around.)
In economics, there’s “This bull market will continue forever.” In the past, all such markets have gone diving among the sharks; but this one is different because [new technology/right party in office/....]. In politics, “My party will rule forever” and “We’re going to simplify the tax code.”
Study cycles: There are “moral panic” cycles; times when drunk driving or gambling is considered a major problem, and others when it’s shrugged off. There are economic cycles; as I write, we’re on the downslope of one. And political cycles; in the US, one swings between parties and another between ideologies. The two political cycles have gone together recently; but don’t count on this continuing.
Look at the future which has already happened: An elementary school teacher looked out at my class, and said we were the largest class she’d ever taught. After us came the Baby Boomers.
When the Boomers overfilled elementary schools, it should have been easy to predict there were going to be a lot of college students not far in the future. Colleges didn’t prepare for the overflow.
Find indicators which work: During the next fifty years, some countries will fall apart. Others will merely undergo revolutions or go bankrupt.
I use male life expectancy at birth as a sign of a country’s stability. The US doesn’t top the list. (This is apparently partly because babies who would be considered dead at birth elsewhere are counted as alive for the few hours they survive. But that’s not the whole story.)
There are things you can’t predict completely. (Or maybe you can — in which case I recommend investing as your fulltime job. Sexual morality will be different fifty years from now — but different how? Vatican III will probably make changes in the Roman Catholic Church — but when will it be held, and what will those changes be? (My guess: Around 2060. About the changes, I can make one confident prediction — some of them will cause schisms.)
What can you do about these?
Have fun: Pick changes you find interesting.
Decide what works best with your story and characters: If it’s useful for your heroine to be a Roman Catholic priest, change church law so this can happen. (I don’t expect Vatican III to allow female priests; but perhaps Vatican VI or Marsport I will.)