that depends on which conspiracy theorist you ask. In reality though, the Catholic Church does not hold a whole lot of pull in the political world, because those in the political world who claim to be Catholic, such as Joe Biden, do not follow the church's teachings, and so are not really Catholic. In other matters though, the Church holds great sway and does great things. The Church is still the largest charity organization in the world, and does quite alot of good for those in need.
Not like they used to be but in some places like Italy they have a lot of power still i suppose. The Catholic Church is worth several billion dollars. Was a time when they ruled the then known world and operated basically as a Theocracy/Oligarchy and a fairly brutal one at that. Fortunately in places like the US they dont have nearly as much political power as they once did. In more catholic regions they still may hold some power in politics but in many states and regions they have none. Many are even quite anti-catholic. The US is heavily protestant (over 50%) and most protestants are opposed to catholic beliefs.