1. How close is too close? Who gets to decide?
As an example, some years ago I had a Fantasy Hero setting that was supposed to be deliberately broad stroke. ...
You could say I was being forward thinking by having one of the African cultures being the most advanced on the planet (they were in what we'd think of as mid-Renaissance when everyone else ranged from Iron Age to Late Medieval) or running to negative stereotypes because the Central/South American expie wasn't a very nice place. I could see someone of Nahua ethnicity who's seen all the Aztecs' negative traits constantly front and center and all their virtues ignored getting kind of soggy about that. So was it a bad idea to even go that far?
So, in good critique, we can note doing well on some things, and worse on others. And while there's some tendency to ask, "Should I not have done that?" I think the better approach is to think on how you can do better next time - how do we continue to improve?
I think any time we are deliberately using broad strokes, we need to examine those strokes, and make sure we aren't leaning into stereotypes too much. And maybe with one of these you did better than the other.
Simple technique I've seen for avoiding this - write down a description of the culture of a given area, in your broad strokes. Check yourself then and see if that matches a stereotype you don't want to propagate. If you see one, you have two options - change the stroke you have, or add a stroke to that culture, that defies the stereotype, giving the whole more depth.
2. What translates into other cultures?
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I'm not suggesting that one shouldn't take care in these cases and others, but I do think the appropriate borders in such things are really unclear in a lot of cases.
They definitely aren't always clear. But, that's not a reason to throw up our hands in despair. It is a reason to think and try to be sensitive.
If you are doing something for your group alone, well, then ultimately you and your table decide. And then it may be good to just be open with your group about what you are trying to do. Maybe they have thoughts about it that can guide you. You can then make it clear that your own awareness of stuff is a work on progress, and you don't have to be perfect on the first shot. You can then maybe relax a bit, so long as you are trying to be better each time.
And I totally get where you are coming from - I'm a white, cisgender heterosexual male. My grandparents immigrated (with my parents, who were children at the time) to the US after WWII, as they came from a place that fell behind the Iron Curtain. I have never been to the Old Country, I didn't even pick up the language, and documentation on the mythology of the Old Country is... basically nonexistent. So, what culture can I validly draw from?
Part of the answer to this can come from consideration of "punching up or punching down". You might respectfully borrow elements from folks who aren't disadvantaged in the cultural scene with respect to you. Someone like me, who is part of a cultural majority here, whose cultural legacy is European, but got swallowed up, might be okay taking inspiration from most European mythologies for my games? I'm on shakier ground if I borrow from African, Native American, Meso-American, Middle-Eastern or Asian cultures. For those, I'd probably want to at least find sources with strong understanding of the cultures in question, and be careful how I use that material.
There's a lot to be said for doing research, and even taking classes, in the cultural legacies you'd like to represent. Go farther then reading Wikipedia.