Both of these are correct, assuming that peoples refers to ethnic groups. However, because people's is very common and peoples' is pretty unusual, the latter can tend to look like a mistake for the former even when it is correctly used. Arguably this is no good reason not to use it correctly, but even so it might sway me towards a wording like (2).
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AlpheccaStarsJust "other cultures" works fine for me.You beat me to it. I was going to say the same thing.