Contradiction with Matthew 7:1
Leviticus 13:23 involves making a judgment on cleanliness, while Matthew 7:1 advises against judging others.
Matthew 7:1: Judge not, that ye be not judged.
Contradiction with James 4:11
Leviticus 13:23 involves speaking to the priest about someone's condition, while James 4:11 warns against speaking evil of one another.
James 4:11: Speak not evil one of another, brethren. He that speaketh evil of [his] brother, and judgeth his brother, speaketh evil of the law, and judgeth the law: but if thou judge the law, thou art not a doer of the law, but a judge.
Contradiction with John 8:7
Leviticus 13:23 is about determining guilt of impurity, whereas John 8:7 speaks against passing judgment unless one is without sin.
John 8:7: So when they continued asking him, he lifted up himself, and said unto them, He that is without sin among you, let him first cast a stone at her.