Parts of both groups will survive for more than 20 years, but less than 200. There won’t be a significant difference with gender, both will face the same issues common to humans.
Namely, the essence of being human is “us” and “them.” Without the presence of an outside group, and even with that, the tendency is to splinter rather than join. It’s mostly been conquest which brings groups together.
It’s not going to take more than a year for rival groups to form. Much less, probably a few months. Since you’re taking only Americans, then there will be the usual suspects. The red states types and the blue states type. The Christians and the nots. Whatever. You won’t start off with classes, but give it time. On the positive side there aren’t any gun holders vs. not. Point is, it really matter how the groups are divided, once they are, they will emphasis their differences.
Madagascar is a huge island, almost the size of Texas, and 10,000 people would just be dots on plains, so one would think that the groups could just take off and never see each other for a zillion years, but we have unmistakable evidence that Skald is truly evil. There’s the Central Shrine which is worth fighting for the death for. A group with access to modern knowledge will be able to decimate a group without.
The other problem is that with the given scenario, the immediate need for cooperation by the entire 10,000 members is minimal. The only real need would be attempt to create cloning, and that would be a several hundred year project for a group this size. It would become impossible when the groups separate and start spending their efforts gaining an advantage over each other.
Without the ability to grow, then each death by accident, murder, war or suicide will decrease the population. With a mortality rate of even 1%, then it’s pretty much over in 500 years. At 2% it would only take a couple of hundred. The only thing which would keep the populations from totally collapsing is that there will be a few bands which will take off to the far sides of the island and live as stone age hunter gatherers. For small bands to survive long term, the requirement would have to be bonds strong enough to overcome the natural jealousies.
Add the frustrations of no opposite sex around, questions of how to divide resources, etc., I don’t think that any of the subgroups or bands will be able to last more than 200 years.