I do not follow. If you play the game regularly your character will eventually be made a bishop and then an archbishop (again, once achieved, these titles are permanent). Your character will also be made a cardinal every now and then (being in the college is strictly a temporary occurrance). There is no way around this. For instance, as of this morning my character ranked #29 among the conservatives in the game. With the current player distribution, the first college of cardinals will be composed of 58 conservatives and 2 liberals, so it is very likely my character will become a cardinal in the upcoming "consistory" (Would that make me a Cardinal Deacon?
Much like in real life (unfortunately), why would you play the game, if you are actively against becoming a hierarch?
If you concentrate your activity in one of the game's archdioceses (Mexico City, Chicago, Boston, Dublin, Manila and New York, so far), it is very likely you will be elected a bishop there and eventually you will be the best player among the bishops of one period and that will make you the archbishop for the next period (regional bishops and archbishops are also named for a period of time and then "retire" right before the next "election", but they can be elected again after a brief period of ineligibility). Again, there is very little you can do to prevent this other than not playing the game.
As for Pope (also a temporary position in the game), the new rules make it much less automatic than it was in Priestville, but I still have to see the new rules in action. The first pontifical election in Vatican Wars is still a couple of weeks ahead.