So, basically, pederasty. And the ones who "give" girls as if they were property and not people are men. Umm, seems that the problem is not polygamy, which among consenting adults might not be a problem. The real problem is someone owning people and forcing them into relationships they might not want. The fact that they previously groomed them to think they have no choice doesn't make it OK. After all, have you asked the girls? They might not like the older men at all.
I think that the practice that feminist find troubling is slavery and pederasty, which is what "give a girl to an older man" means. The girl is not deciding for herself, not given choices in case she doesn't want that.
The fact is that many times, within the non-western culture, girls and women aren't OK with those practice. But in that culture, they don't hold power to refuse, neither are given voice and, interestingly enough, not are listened by the western men who try to say that they "just have different values".
After all, western feminism comes from western patriarchy, where young women were given by their fathers to other men, usually older. And feminism is those women saying "I'm not ok with this and don't want that for my daughters".
So in those tribes, what are the girls saying? Do they want to come back to that? no?
Other cultures have their own versions of feminism. Of course, to learn about those versions, you need to listen to the girls and women there, not just the older man who is perfectly happy with his teenager wives.
Hell, Kamasutra has a part were they splicitly talk about unhappy wives and how to deal with those unhappy wives. One of such advices was "make sure they don't become friends". Quite cruel if you ask me.