Can a Bad Person Really Change?

Can a bad or evil person change, find religion, and become a good person who serves God? This seems hypocritical to me.

Jesus said that all men must be born again.

"Jesus answered and said unto him, 'Verily, verily, I say unto thee, except a man be born again, he cannot see the kingdom of God'" (John 3:3 KJV).

To be born again means your spirit, the real you, dies and is born anew. You actually become another person.

I (Paul and all Christians) am crucified (put to death) with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.
(Gal. 2:20 KJV)

Therefore if any man be in Christ (born again), he is a new creature: old things are passed away; behold, all things are become new.
(2 Cor. 5:17 KJV)

When a person calls on the name of the Lord and is born again (Rom. 10:8-17), the person he was dies. A new person is born on the inside and created in the likeness and image of Jesus (Eph. 4:24). He then has the ability to live as a good person, not a bad one. However, this is usually accomplished by the process of renewing one's mind by the Word of God.

Jesus called a sinful tax collector to be one of His disciples, and then He ate at his house. Notice the reaction of the religious people:

But their scribes and Pharisees murmured against his disciples, saying, "Why do ye eat and drink with publicans and sinners?" And Jesus answering said unto them, "They that are whole need not a physician; but they that are sick. I came not to call the righteous, but sinners to repentance."
(Luke 5:30-32 KJV)