'have yet to ...' means the same as 'hasn't yet ...' The winner hasn't been announced yet. The winner has yet to be announced. Notice that with the negative we use the past participle (3rd form) as is usual with present perfect. But with the positive form, we use to + infinitive. We could also say: The winner is yet to be announced. So this construction comes from an older form of English, and that's why it sounds a bit strange (and is not so common). Koopa, I think the tense is correct, but it's not so well written. It would have been better to say: Although thousands of people now identify themselves as ... But I think the point is that they choose to be identified as Taino, rather than someone has labelled them this.

"yet" has two different meanings. The way you are using it in this sentence means it has not happened up to this point in time. The other meaning means at the same time. For example: "While it may be cold outside it is not yet winter." "You said you did not have money yet you bought a drink"

The sentence isn't a problem. You can use those words, but then the sentence doesn't feel right to me unless you change identify to identified. I may be wrong, but I think it changes the tense from present to past. "Although thousands of people 'are now identified' as Taino, the tribe 'hasn't yet received' official government recognition or the federal benefits that accompany it."