If the show or movie involves subject matter of a moral nature that I do not agree with, and one that Netflix did not fund or produce, I would not cancel service.
If a show or movie involves subject matter that is both immoral and illegal,( such as pedophilia) and one that Netflix has funded and made available under the auspices of encouraging others to perform the same kinds of actions, I would cancel service and possibly engage in direct legal contact with Netflix.
John Donne said it very well.
No man is an island,
Entire of itself,
Every man is a piece of the continent,
A part of the main.
If a clod be washed away by the sea,
Europe is the less.
As well as if a promontory were.
As well as if a manor of thy friend's
Or of thine own were:
Any man's death diminishes me,
Because I am involved in mankind,
And therefore never send to know for whom the bell tolls;
It tolls for thee.
As individuals, we are in the world. As individuals, we don't have to take part in illegal and immoral activity. Subscribing to Netflix and other services that make available some content that some of us find questionable or personally wrong, does not in and of itself, show or suggest, that all subscribers of said services are in full agreement with all content offered.
As an individual and Christian, it is not my place to dictate to others what they should or should not watch with any given service, nor is it my duty to try and control what other consenting adults do in the privacy of their own homes etc. What is my duty is to live my life with honor, respect and help others when I can, and try and be an encouragement to everyone one I can, whether in word or in deed.
If you are a person that struggles with watching things you know you shouldn't on Netflix or elsewhere, the logical thing to would be to remove yourself from the temptation, at least and until you can exercise more personal control and self-responsibility.
When struggling to find objectivity in a question, remove the emotion from the subject and you will be able to find the answer much more clearly.