If the subject is "every people", should we use "every people has their own preferences", or "every people have their own preferences"?

I think it should be have because of "their", but I've heard that the sentence "everyone has their" is correct.

What is the explanation for these usages?
"every people" is wrong.

"every person / everyone has his or her own preference" -- preferred in careful English
"every person / everyone has their own preference" -- commonly heard; grates with some people
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Every people has their own culture.

Thanks, but that's not an explanation