IMHO, the answer to this three-part question is very simple.
Q: Has religion failed in its goal to unite believers?
A: No, because by definition religion serves to divides us. It does not unite us. The mistake is to presume that Islam is a religion, when it is a deen. Islam would not fail to unite us, if only we actually followed it.
Q: Does ethnicity tinged with sectarianism trumps faith?
A: Ethnicity and sectarianism are both forms of division, and division is all about self-interest (and thus is shirk). Faith - that is religious faith - does not unite us.
Q: Does religion take a back seat when it comes to self interest? If so, why?
A: See answers 1 and 2.