Should Christians work for people who knowingly lead a sinful life?

The answer depends on many factors. It isn't so much a "you should/shouldn't" but rather "is it the wisest choice?"

 #1 How close is the employee/employer relationship going to be? We are not to be unequally yoked with unbelievers. While this often is used specifically as an admonition not to marry unbelievers, it actually it also applies to any contractual relationship or close tie where we are supposed to be headed in the same direction as another person. (II Cor 6:14-18) If you are offered a position as co-CEO, but your future partner has some unethical business practices, you may wish to decline unless your new authority is going to give you enough influence for change. If you are seeking a new roommate, but an applicant is a known drunk and partier, you should probably move on. If you know a potential boss will interfere with your daily life and force you to compromise your faith, then that isn't a healthy work situation, etc. The general work situation doesn't usually force such close ties, so this is not always an issue - but consider how much you will be "yoked" to the job.

 #2 How much is your reputation and witness tied in to the business? This again is not usually an issue, but it can be. If your job is, say, a Planned Parenthood rep, then you are going to get linked to abortion even if you are just a receptionist. If you work for Playboy, then you will get linked with fornication and pornography, etc. Most christian parents will be a bit disturbed if their daughter decides to work at a bikini Batista or as a lingerie model. To a broader extent, even working closely with organizations that attack the christian faith or support lifestyles of sin can affect our testimony or tempt us into sin ourselves. Use your own conscience for this, though. If your dream job is a bartender or working at a meat shop, don't be too disturbed if some teetotalers or vegetarians disapprove. [Just don't demand they in turn be ok with it or meet you for lunch at work].

 #3 Will the job greatly interfere with your spiritual life? Some jobs require work on Saturdays or Sundays, making it difficult to attend a specific time of worship. Other jobs may have such a secular or anti-christian environment that you find yourself struggling to stay spiritually afloat. You may join in their sins such as gossip or slacking-off. While most obstacles can be overcome (meeting with Christians at an alternate time for worship or a small group, getting an accountability partner, etc) - there will be times where the job becomes the biggest stumbling block to spiritual growth. In such cases, it may be best to cut ties and trust God to provide.

There is nothing sinful in working for an unbeliever in and of itself. Scripture has many cases of people who did so (Joseph and Daniel, for instance, though they didn't have as much choice). Also, we may find ourselves working under a commander or leader whom we don't agree with. In these cases, we are responsible to submit to authority, and the leader is responsible for the choices he makes. We are supposed to be in the world but not of it, so we shouldn't avoid work or volunteering for the sole reason that the boss is an unbeliever.