Both cities have ethnographic museums.
I only saw that in Frankfurt, it was very disappointing. Although they have a large collection, some are only displayed during special exhibitions as they have very limited exhibition space.
Munich has permanent exhibitions, it says on their site, see for yourself if there is an interesting area for you, they are briefly introduced there.
Here the home page from the "Museum 5 Kontinente":
https://www.museum-fuenf-kontinente....h-summary.html
And here the home page from the "Weltkulturen Museum" in Frankfurt:
https://www.weltkulturenmuseum.de/en/
The page is also in English, like given.
Enjoy your stay in Germany!

Regards,
Detlef