In Guns, Germs, and Steel, how does Diamond's perception of the function of religion in a kleptocracy make the mission for Catholics difficult?
the answer can be found in chapter 14: From Egalitarianism to Kleptocracy.
The meaning of your question is a bit unclear. Diamond's perception of religion really does not have an impact on Catholics unless they believe Diamond's thesis. The existence of Diamond's thesis does not force Catholics or anyone else to behave in any given way. It's also not clear as to what you mean by "the mission for Catholics." I will talk in this answer about what Diamond says the role of religion is and then try to suggest ways to connect that to Catholicism.
Diamond argues that religion is used by the leaders in societies to justify the power that the leaders have. The leaders create "kleptocracies," in which they take things from their people through taxes or tribute. They need a way to justify what they are doing and a religion that says that they have the right to do this (perhaps because God has given them that right) is helpful. Diamond also argues that a religion tends to create social solidarity among people who are not related and, therefore, who have no reason to care about one another.
If you believe this, it makes it harder to perceive the mission of the Catholic Church (particularly in the past) as one that is wholly good. The Catholic Church has been closely connected to the rulers of various countries at various times (crowning Holy Roman Emperors, for example) or has actually ruled in a temporal way (in the Papal States). If Diamond's thesis is true, then the Church has simply been acting as (in Marx's words) the "opiate of the masses," making them willing to let their leaders steal from them. If you believe this, it makes it hard to truly embrace the historical role/mission of the Catholic Church and to think that it has been a force for good.