Jesus, the Law, and the Gospel of the Kingdom

I have noticed, especially in the context of some discussions regarding issues of marriage, divorce, and remarriage (MDR), a recent tendency to see Jesus only through the prism of the Law of Moses. Some are teaching that Jesus and Moses taught the same thing regarding marriage matters, along with all other things.
This is not a perspective that one would gain from the account given in Matthew 19:1-9, wherein Jesus first appeals to "the beginning" and then declares that Moses gave the law regarding divorce because of the hardness of the heart of Israel, but that "from the beginning it has not been so" (Matthew 19:8).

This perspective comes more from a particular interpretation of Matthew 5:17-18, and assumptions that underlie that interpretation:

"Think not that I came to destroy the law or the prophets: I came not to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass away, one jot or one tittle shall in no wise pass away from the law, till all things be accomplished" (Matthew 5:17-18).

Many reason from this statement that since Jesus is not going to adapt the Law in any way, everything which He will say will be in accordance with that Law.

Such an interpretation may make sense on the surface, but when one begins to investigate what Jesus continues to teach His disciples and the crowds around Him, many inconsistencies become glaring.

"Ye have heard that it was said to them of old time, 'Thou shalt not kill;' and 'whosoever shall kill shall be in danger of the judgment': but I say unto you, that every one who is angry with his brother shall be in danger of the judgment; and whosoever shall say to his brother, 'Raca,' shall be in danger of the council; and whosoever shall say, Thou fool, shall be in danger of the hell of fire. If therefore thou art offering thy gift at the altar, and there rememberest that thy brother hath aught against thee, leave there thy gift before the altar, and go thy way, first be reconciled to thy brother, and then come and offer thy gift" (Matthew 5:21-24).