Dear N:

You wrote:

 Which of these sentences are correct? They are all supposed to mean: “Just because a man hated the victim of a crime does not mean he is guilty. We know that he hated the victim, but we cannot conclude from that that he is guilty.”

1-A man is not guilty because he hated the victim of a crime.

This is OK.

2-A man is not guilty SIMPLY because he hated the victim of a crime.

This is better, perhaps more common would be JUST instead of SIMPLY, but either is fine.

3-It is not because he hated the victim of a crime that a man is guilty.

This is technically OK, but it is hard to follow.

4-It is not SIMPLY because he hated the victim of a crime that a man is guilty.

This also is technically OK but harder to follow.