If I was doing Greyhawk first thing I'd do is cut the number of nations by about two thirds. There's way too much repetition, the place is far too balkanized.
Nyrond and Furyondy even sound similar, pick one. One type of barbarian will do, frost, ice and snow is two too many. One Arab nation, not three. Don't need both Rel Astra and Greyhawk, so the former has to go. Get rid of all the little crap around Keoland. Sea Barons or Sea Princes, pick one. Etc.
Keep the good stuff only, such as the Free City of Greyhawk, Iuz, Great Kingdom, Scarlet Brotherhood, Theocracy of the Pale, one of the good guy nations, etc.
When to set it is tricky. The classic prelude to war period is best for a rpg campaign setting, but it smacks of the Cold War, not the 2010s.
Relevance:
1. More female rulers and NPCs.
2. Environmentalism vs commercial development. Environmental disaster, perhaps represented by magic gone awry while attempting to control elemental forces such as giants or the Temple of Elemental Evil.
3. Economic decline, possibly due to the aforementioned disaster. Hits City of Greyhawk hard. Many made homeless.
4. A new, good-aligned ruler comes to power in the Great Kingdom. Ends war, forges diplomatic ties with good-aligned nations.
5. Minor wars still rage. With the Baklunish if you want to be super-obvious. Savage humanoids in their mountain strongholds would be another option. Or perhaps dwarves.
The world I recently made up for a session at the weekend had economic decline in a Roman/Holy Roman-style empire, and commercial exploitation of the environment as its big issues. Both were probably unconscious on my part.
<- Relevant
No, no, a thousand times no.
Do this and you'd kill many of the aspects of the setting that attracted fans to it in the first place. For one thing, having those multiple similar nations adds a subtle layer of realism to the setting. To a North American like me, the nations of places like the Middle East, Africa and South America all seem fundamentally the same, but as anyone who actually lives in those continents will tell you, every country has its own distinct traits and variations, howevermuch they might be similar in other ways. The same thing applies to English-speaking countries, when you see the cultural differences that separate the United Kingdom, Canada and the United States, and the differences each has within its own borders. They might seem fundamentally the same to an observer from Asia or South America, but people who actually live here know how untrue that is.
Having so many of these different nations around allows DMs to engineer conflicts between them, or to play up shades of grey-is Keoland a benevolent overlord to ungrateful surrounding territories, or does it unfairly use its military and diplomatic power to bully its neighbours? Can Urnst and Nyrond honestly get along with one another, or are they constantly seeking to undermine each other due to a history of mutual repression and recrimination? What happens when the nations of the Iron League are at loggerheads over matters of trade-how do Idee and Onnwal maintain their alliance when they're competing for favorable trade and military alliances with Greyhawk and Keoland?
Good and evil fundamentally exist in Greyhawk, but the lines are often much blurrier than you'd think. Evil forces will fight each other as much as they do the good guys, the good guys themselves will jockey for power and position the way allied nations tend to do in the real world. Just look at how the United States has butted heads with its European allies during World War II, the Cold War and even today.
As for "relevance", arbitrarily adding more female rulers reeks of simple political correctness. If you read my own works at Canonfire, you'll find that discrimination against women and/or demihumans is perfectly legal even in places like the Yeomanry, Ratik and Nyrond. I certainly don't endorse these types of attitudes, but I do want to emphasize that Greyhawk is far from being a perfect world. Indeed, it can add make for interesting role-playing challenges if female PCs have to prove themselves along the lines of Jeanne of Arc, Marie Curie or Empress Maria Theresa, women who all had to prosper in times and areas dominated by men but were able to do so through their own talents. This is something many women even today will be familiar with, too.
As for minor wars raging, this happens all the time in Greyhawk. From Gygax onwards, published materials are full of references to raiders, invasions, and brewing wars. Not to mention that many of these wars can be nipped in the bud by daring bands of heroes-indeed, this was arguably one of the points of
Against the Giants, namely to thwart an impending giant invasion by slaying its leaders and striking at their home bases before they are ready to strike. In my own version of the Greyhawk Wars, the successful completion of these adventures decapitated the leadership of the impending giant invasions. The giants still attacked, but they had no leadership and no coordination, and so they ultimately failed to conquer Geoff or Sterich. Both nations emerged from the Wars battered and bloodied, but victorious.
As for the rest of the "relevant" parts, I'd say that if you're going to introduce real-world themes, you need to do it subtly. There's nothing I hate more than fiction of any type that beats you over the head with the symbolism and the message-and some of the things proposed here, like a new king taking control of the "evil empire" and ending the war-cut way too close to overtly political themes, and that could put off more conservative players.
One thing I'd view as absolutely essential is for liberals and conservatives alike to be able to enjoy fiction, whether it's comic books, TV or fantasy games.