It is a central part of Christian theology that Jesus was sinless, which means that he kept the Torah perfectly, so if you think that he broke the Sabbath, then you should think that he was just another sinner who was in as much need of a Savior from his sin as the rest of us. Furthermore, the way that the Bible instructs us to tell that someone is a false prophet is if they teach God's people against obeying His commands (Deuteronomy 13:4-6), so if you think Jesus taught against obeying God's dietary laws, then you should consider him to be a false prophet. Likewise, it is a sin to add to or subtract from God's commands (Deuteronomy 4:2), so if you think he tried to subtract God's dietary laws, then you should consider him to be just another sinner who could not even save himself much less anyone else.
However, according to the Pharisees, if you didn't obey their traditions for how to keep the Sabbath, then you were breaking it, so while Jesus certainly broke their traditions, he never broke the Sabbath as it was intended to be followed. In regard to Mark 7, the topic of conversation was that you could be defiled by eating kosher food with unwashed hands and Jesus was simply denying that to be the case. His statement in Matthew 15:20 shows that at the end of the conversation he was still talking about not being defiled by eating with unwashed hands, so he never jumped topics from speaking against a man-made ritual purity law to speaking against obeying God. In
John 8:1-12, we have another example of Jesus following the law rather than breaking it. There was no judge to pronounce a sentence (
Deuteronomy 19:17-21), there was no man accused (
Leviticus 20:10), he didn't have any witnesses to examine (
Numbers 35:30,
Deuteronomy 19:5), and he did not have a confession, so if he had condemned her, then he would have acted in violation of the law. Just a few verses later Jesus said that he judged no one (
John 8:15) and he also said that he came not to judge (
John 12:47), so he did not exercise authority as a magistrate and did not condemn her, but he did recognize her action as sin, and told her to go and sin no more.
The problem is with your theology not mine:
Joh 5:8 Jesus saith unto him, Rise, take up thy bed, and walk.
Joh 5:9 And immediately the man was made whole, and took up his bed, and walked: and on the same day was the sabbath.
Joh 5:10 The Jews therefore said unto him that was cured, It is the sabbath day: it is not lawful for thee to carry thy bed.
Joh 5:11 He answered them, He that made me whole, the same said unto me, Take up thy bed, and walk.
Joh 5:12 Then asked they him, What man is that which said unto thee, Take up thy bed, and walk?
Joh 5:13 And he that was healed wist not who it was: for Jesus had conveyed himself away, a multitude being in that place.
Joh 5:14 Afterward Jesus findeth him in the temple, and said unto him, Behold, thou art made whole: sin no more, lest a worse thing come unto thee.
Joh 5:15 The man departed, and told the Jews that it was Jesus, which had made him whole.
Joh 5:16 And therefore did the Jews persecute Jesus, and sought to slay him, because he had done these things on the sabbath day.
Joh 5:17 But Jesus answered them, My Father worketh hitherto, and I work.
Joh 5:18 Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God.
Did Jesus work on the Sabbath day? Did he tell the man to do something that would have gotten the man killed in Moses day? Yes, did you not read how a man carried sticks on the Sabbath and was stoned for it?
Num 15:32 And while the children of Israel were in the wilderness, they found a man that gathered sticks upon the sabbath day.
Num 15:33 And they that found him gathering sticks brought him unto Moses and Aaron, and unto all the congregation.
Num 15:34 And they put him in ward, because it was not declared what should be done to him.
Num 15:35 And the LORD said unto Moses, The man shall be surely put to death: all the congregation shall stone him with stones without the camp.
Num 15:36 And all the congregation brought him without the camp, and stoned him with stones, and he died; as the LORD commanded Moses.
Num 15:37 And the LORD spake unto Moses, saying,
Num 15:38 Speak unto the children of Israel, and bid them that they make them fringes in the borders of their garments throughout their generations, and that they put upon the fringe of the borders a ribband of blue:
Num 15:39 And it shall be unto you for a fringe, that ye may look upon it, and remember all the commandments of the LORD, and do them; and that ye seek not after your own heart and your own eyes, after which ye use to go a whoring:
Num 15:40 That ye may remember, and do all my commandments, and be holy unto your God.
Num 15:41 I am the LORD your God, which brought you out of the land of Egypt, to be your God: I am the LORD your God.
You still think Jesus kept the Sabbath?
Hear again how Jesus broke the Sabbath:
Joh 9:1 And as Jesus passed by, he saw a man which was blind from his birth.
Joh 9:2 And his disciples asked him, saying, Master, who did sin, this man, or his parents, that he was born blind?
Joh 9:3 Jesus answered, Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him.
Joh 9:4 I must work the works of him that sent me, while it is day: the night cometh, when no man can work.
Joh 9:5 As long as I am in the world, I am the light of the world.
Joh 9:6 When he had thus spoken,
he spat on the ground, and made clay of the spittle, and he anointed the eyes of the blind man with the clay,
Joh 9:7 And said unto him, Go, wash in the pool of Siloam, (which is by interpretation, Sent.) He went his way therefore, and washed, and came seeing.
Joh 9:8 The neighbours therefore, and they which before had seen him that he was blind, said, Is not this he that sat and begged?
Joh 9:9 Some said, This is he: others said, He is like him: but he said, I am he.
Joh 9:10 Therefore said they unto him, How were thine eyes opened?
Joh 9:11 He answered and said, A man that is called Jesus made clay, and anointed mine eyes, and said unto me, Go to the pool of Siloam, and wash: and I went and washed, and I received sight.
Joh 9:12 Then said they unto him, Where is he? He said, I know not.
Joh 9:13 They brought to the Pharisees him that aforetime was blind.
Joh 9:14
And it was the sabbath day when Jesus made the clay, and opened his eyes.
Joh 9:15 Then again the Pharisees also asked him how he had received his sight. He said unto them, He put clay upon mine eyes, and I washed, and do see.
Joh 9:16 Therefore said some of the Pharisees, This man is not of God, because
he keepeth not the sabbath day. Others said, How can a man that is a sinner do such miracles? And there was a division among them.
Do you not understand that the laws of the old covenant are not what Jesus lived by? How can you be a follower of Christ and not understand what I am talking about?