There are no "builders" as this is a word picture referring to an ancient building technique1:
The idea is that when a house is built, the builders examine each stone for suitability, and the unsuitable stones are thrown away. So the Psalm is referencing this technique by saying "YHWH will take the stone that has been discarded and make it a cornestone for his house" (as suggested by verse 19)
Thus asking "who are the builders?" is a like responding to "a bird in the hand is better than two in the bush" by asking "which bush?"
However we can try to read more meaning into this verse by looking at the context. Supposedly the stone is viewed as flawed by someone examining it, who rejects it. Let's look at the rest of the Psalm
The LORD is on my side; I will not fear:
What can man do unto me?
The LORD taketh my part with them that help me:
Therefore shall I see my desire upon them that hate me. (KJV)
This is similar to the statement that "what man rejects, God accepts"
Then we have verse 8:
It is better to trust in the LORD
Than to put confidence in man.
Aha! A theme is developing..
It is better to trust in the LORD
Than to put confidence in princes.
So we are certain of the theme, which is common in Psalms, that God is the salvation of those who trust in him. It is this concept of deliverance that is illustrated by God taking the rejected stone and putting it in a position of pre-eminence, however more than just deliverance is meant. The fact that the stone was rejected points to a spiritual principle, e.g. just as the waste of the animal kingdom is the food of the plant kingdom and vice versa, the rejected ones of the kingdom of men are the important ones in God's kingdom. See, e.g. 1 Cor 4.13 has "...we are made as the filth of the world, and are the offscouring of all things unto this day." So both concepts are present in this verse.
But like all the other Psalms, the whole point is for the reader to trust in God for deliverance from whatever enemies they happen to be facing. Psalms are homiletic works intended for application by the worshipper.
It is in this sense that Jesus applies Psalm 118 to the husbandmen in charge of the vineyard in Matthew 21:42-45. It was understood that the vineyard was a type for Israel, and the husbandmen would be the religious leadership of Israel -- not "jews", which were the vineyard, but the husbandmen tending the vineyard:
Matthew 21:45 (KJV)
45 And when the chief priests and Pharisees had heard his parables,
they perceived that he spake of them.
However Jesus didn't just apply this verse to point out that God would deliver him from the hands of the religious leaders - that was just a secondary point. Jesus went on to threaten the leaders:
Matthew 21:44 (KJV 1900)
44 And whosoever shall fall on this stone shall be broken: but on
whomsoever it shall fall, it will grind him to powder.
So the choice is to be broken or to be utterly destroyed. If you were broken then you would be the offscouring of the world and rejected, making you suitable for God's kingdom. Otherwise you would be destroyed. There is no more choice to go on as you did before. That is, it would no longer be possible to reject the stone and have God take it away. How could a cornerstone crush someone? By filling the whole earth:
Daniel 2:34–35 (KJV 1900)
34 Thou sawest till that a stone was cut out without hands, which
smote the image upon his feet that were of iron and clay, and brake
them to pieces. 35 Then was the iron, the clay, the brass, the silver,
and the gold, broken to pieces together, and became like the chaff of
the summer threshing floors; and the wind carried them away, that no
place was found for them: and the stone that smote the image became a
great mountain, and filled the whole earth. (KJV)
So Jesus is taking Psalm 118:22 and combining it with Daniel 2:34, in his prophecy against the leadership of Israel, but this does not mean that Psalm 188:22 can only be used in this one homiletic application. It can be used as a homily in many different ways, by people who have been rejected by the world and trust in God for deliverance. So we do not want to say Psalm 118 was referring to Pharisees and Sadducees, but rather that Jesus used Psalm 118 in this way.
- Frank-Lothar Hossfeld and Erich Zenger, Psalms 3: A Commentary on Psalms 101–150, ed. Klaus Baltzer, trans. Linda M. Maloney, Hermeneia—A Critical and Historical Commentary on the Bible (Minneapolis, MN: Fortress Press, 2011), 241.