Q: Do Poor Bonus and Rich Bonus contradict each other, such that only one can be in play at a time?

A: No, they do not contradict one another, though they’re guaranteed not to apply to the same player at any given time. One person might have the fewest Keepers, and take that Bonus, while another player has the most, and takes that Bonus.

It IS possible, however, for one’s status as Richest or Poorest player to change during one’s turn such that one may start as the Poorest player, get to take the Poor Bonus (drawing 1 extra) then subsequently during one’s turn, play enough Keepers to become the Richest player, thereby getting to take the Rich Bonus (an extra play). One might also lose Keepers and switch status the other way, though you’d wouldn’t be able to actually utilize the Rich Bonus if you moved that direction.

Also keep in mind that in the case of ties, no-one gets the bonus.

It’s totally reasonable and possible for them to be in play together without contradicting.