My point is theme, lore, style, and preference are separate thingd. You can tie them together or not.
Gotcha. I don't think they're as separate as you want to make them. Style and theme pretty lore dependent.
Going with the greek theme, if I say there are centaurs and satyrs, I don't have to come up with lore for it since the theme itself is the lore. Everyone(or at least most gamers) know that those are greek mythology themed creatures, so they're expected in such a setting. If however, I want to add in gnomes, it's going to be pretty out of theme and should have some lore explanation for why this greek themed setting has gnomes.
Preference isn't dependent on lore, but it's better if there is lore of some sort, either inherent like centaurs in a greek themed setting, or created for the gnomes in the greek themed setting. As has been noted, while it's valid to just be like "because I said so," it's often unsatisfying to hear that.
For example, you can say your has a Greek Mythology theme. But the lore can be altered to offer all kinds of races.
But not all races. I can say I have a reptile theme and allow lizard men, yuan-ti, tortles and dragonborn, but if I then also allow elves, dwarves, halflings, gnomes, humans, tieflings, aasimar, genasi and whatever the rabbit people are called, I no longer have a reptile theme.
I might get away with offering one of those races, but that would be about it. Any more and now I'm offering 50% of the reptile races and I no longer really have a theme.
There's some leeway, but not a huge amount.
Kratos is from a Greek Mythology themed IP. But the lore has him in Norseland. And Marvels Thor interacts with Greek gods. Same with American Gods. Or Dresden Files.
Sure, but none of those is greek themed. You intermix to an extent if your theme allows it. Let's say Jim Butcher had space aliens invade earth in the next Dresden book. That book would be very out of theme.