What things can these GMs do during world-building to defeat a bias toward making cultures white and to make their own game worlds more inclusive?
Most, if not all, my game world spring from historical settings or a mix of several. As such, a lot of the ethnicity comes with the history. If I take Meiji Japan as a base, chance are most people will be Shino-Japanese looking. If I base it on Byzantium, most will have olive tones to their skin.
There is a reason why skin changed colour: the amount of sunlight you get. So, setting a world in hot deserts will naturally lead to darker skin. Having a way to map early species migrations might help you determine what shades got where.
Use different cultures
Ages ago, my players wanted to play an Ars Magica game in Bosia. I knew exactly nothing about Bosnia but that there was a civil war there. So, I went to the library, got some books, and did research -- wow, I just outed that I am ancient. Now a days, it's easier to do via the internet. So, new and weird cultures are everywhere: just trawl through some pages and pick things to add to your game world.
In science fiction, the ethnicity of the colonist and the environment where they are will greatly impact their culture: do they grow rice (more communal) or wheat (more individualistic)? Is it post scarcity where you can change body like you change gloves?
Use a random NPC generator
I have one (it's not github, there's a re-write in progress) that creates random NPCs with random ethnicity. When I want an NPC, I roll one. Clearly, the ethnicity probability is based on my game world: If I run a game set in the XIIth century in Norway, chances are slim you will meet someone from the Aztec stock.
This forces some randomness and avoids my own in-build prejudices to come out.
Monsters with a twist
I do tend to give my monsters a reason why they are monsters very much akin to the the dragon of Enoshima. Everyone has a reason to do evil. The orcs attacks the humans because the humans not only desecrated the holly forest but killed many sacred stags. Which they then eat! I mean, who does that? Now, the orcs are led by their owe racists bigoted priest and the voice of reason is gone. Can the PCs help?
In most game words, it is possible to pervert the monsters to become good: In MERP, a tribe of orcs who discovered they are corrupted elves and try to purge their evil. In Cyberpunk, a yakuza rising to the top to unite the clans and bring peace.
There's a poster at a school I saw: "Some people are gay, get over it"
Add gay characters of either gender but make it obvious only when it helps the story go somewhere interesting. Gayness is not a badge of honour, neither is it shameful. It just is. Ringil from a Land Fit For Heroes is a near perfect character where him being gay enhances the story and impact greatly on the rest of the cast: some for good, some for ill.
A romantic encounter between a player and a gay lover might be a great way to lead the story in some interesting direction.
In transhuman settings, changing sleeve to one of a different gender or no gender at all is common. The Takeshi Kovacs Novels do that all the time. This is a perfect way to explore differences between genders: what if you male character gets sleeved into a pregnant woman's body? Who do they cope with it? … Clearly, an interesting story thread.
As your players to go and explore different cultures and ethnic backgrounds. Maybe ask them to play someone of a different culture and ethnic background as they are. Make them do some research!
What things can these GMs do during play to make the world feel more diverse and less culturally monotonous to the players?
Food & Drinks
Describe weird and interesting foods from Indian rice balls to eat eating your plate. If you are brave enough, cook it and sever it to your players. Most of us will leave next to a supermarket that caters to whatever immigrants live nearby. Go there, try stuff.
There is a metric f** ton of free ethnic music on the Internet. Some will make your ears bleed because it is horrid but most of it will add some spice to your game. Capoeira is done to music and can introduce a weird martial art to your setting: I really want to see zero-G capoeira! Taiko drums makes from some great combat music.
Random NPC generator…
Wait, that's already covered but worth repeating. If you have a bias (and we all do), use something random. That mercenary leader you want to annoy the PCs now turned up as a lesbian amori transwoman. Why not?…
Some people are religious and adding those to your setting makes them richer for it. Maybe the crew of the ship that rescued the PCs are all Muslims? Maybe the innkeeper is a Christian in secret? How about Tibetan demon worshippers?…
There are dozens of real world religions that you can draw on, plus hundreds of mythical ones.
Diversity should not be a condiment, added here and there, to make ones work trendy, edgy, and holier-than-thou:
It should matter within your own setting.
It is fine to have a white centric game if the game is set in Viking Norway, just as it is fine to have a full Japanese cast in a game set in Shengoku Japan. Neither should prejudices and racism not play a part in your game world: exploring those is an interesting: Schindler's story is prime example of that.
Within the RPG context, diversity should enhance whatever story you are telling. This is the TL;DR of my answer.