Jesus one time replied to a questioner: You do greatly err, not knowing the scriptures nor the power of God.
The Lord God does not approve of murder. Anyone's murder.
The teachings in the Old Testament... we call it The Law.... are to instruct us in righteousness, to teach us the difference between the clean and the unclean, between holy and unholy.
God gave us what we call the 10 Commandments, which include no murder, and no adultery, among other things. The purpose of the 10 Commandments is to shine light on what is acceptable to God and what is not. And Jesus said if you break one, you break them all. Which means, sadly, we all have done things that are unacceptable to God.
God has one standard: Perfection, holiness, righteousness. The penalty for all else is death....."The wages of sin is death."
Oops..... that means me. And no doubt that means you, too, seeing how you are not perfect either.
So, yes, adultery, homosexualtiy, disrespect toward parents, murder were all under the death penalty..... not that which comes from revenge, but a corporate penalty, not motivated by hate, but by law. BUT.......
But God had and has a plan to extend mercy and grace to all who have fallen short of that perfection he requires. Yes....Jesus himself is the very seat of mercy. He took our death penalty for us. And a good thing, too, or I would have been stoned by now!!!
So, NO Jesus does NOT approve of Matthew's murder. Nor does he approve of your or my lying, worshipping idols, coveting other people's stuff, etc. Oh, but what he does approve of is our admitting we really messed up, and asking for his forgiveness, mercy and grace.... which he has already abundantly supplied.