If you sign on to a production without knowing whether or not it has what you consider to be objectionable material, then you might not have done your due diligence about what it is you will be working on.
In a couple cases I know of second hand, animators voiced their concerns over certain scenes, and those scenes were reassigned by a more or less understanding supervisor and they were given other shots to make up the workload. It happens sometimes in adult TV animation. Not everyone is okay with working on scenes with sex, drugs, or violence. Your scruples might not line up with the show but there are ways you can still keep that job, and most bosses would rather reallocate your effort than lose a valuable worker.
If you make clear your position first with your employer, I don't see why it has to be a cause for contention unless the material as a whole is problematic for you. In that case, you should either bite the bullet and try to reach the mentioned kind of compromise, or seek out another job.
Most people in the business will make an effort to be accommodating if they want you on the show, but you also have a responsibility to yourself and your employer to accept work you can perform with mutual satisfaction.