For one, Catholic Priest are bound by canon law not to participate in politics.
They are not to play an active role in political parties or in directing trade unions unless, in the judgement of the competent ecclesiastical authority, this is required for the defence of the rights of the Church or to promote the common good.
I have heard, from a Jehovah's Witness, that they are not able to participate in politics either.
However, it seems to me that the laity, has a duty to his neighbor to participate in politics. To seek political office if necessary for the purpose of upholding the common good.
Politics should not become an occasion of sin, as it often does through graft and sexual impropriety. Seeking political office doesn't need to be about ambition, as it often is. Running for office doesn't need to be about smearing your opponent, but it often is.
So in essence, most of politics is dirty, that's what Jesus refers to quite often as 'the world'. That is 'the world' that you're supposed to hate. But, we have a duty to build up the kingdom on earth as much as possible, we have a duty to protect and defend the babies in the womb, children in poverty, drug abusers etc.. and very occasionally, laws need to be passed, or more often repealed, for us to carry out our mission as Christians.