Jesus wasn’t trying to start a new religion. Matthew is making it clear to his Jewish audience that the law and the prophets weren’t going away; Jesus was just interpreting them anew. Perhaps he was just trying to get us to listen to the law in our hearts!
As Christians we don’t adhere to the Mosaic law, but we’re still an audience of this Gospel text—albeit a contemporary one. And Jesus was clear when he said the entirety of the law boiled down to love of God and love of neighbor. After all, the law taught the Jews how to relate to God and to one another. That is something we can understand as 21st century Christians. For us Jesus becomes an embodiment of God’s law, exemplifying the love of God and neighbor. And as people for whom Christ is their name, we are called to embody this, too. Every day.