A ‘touchstone’ is a stone used to test the quality of gold alloys: the word is used for a standard against which other things are compared.  Until Jesus, the Old Testament law was the only standard, and religious leaders assessed people's righteousness by how well they obeyed it. But it could only condemn those who fell short: the law could never make sinful people righteous and the sacrifices could never take away sin (Hebrews 10:1-10).

However, the Old Testament also referred to a different standard: a stone or rock which would determine those who were acceptable to God and those who would be rejected.  God Himself is that Rock (Deuteronomy 32:4 says, "He is the Rock, His works are perfect, and all His ways are just.  A faithful God who does no wrong, upright and just is He.").
 
In today's verses, Jesus referred to Himself as the stone described in Psalm 118:22 - the Messianic Psalm chanted by the crowd during His triumphal entry into Jerusalem.  That stone was rejected by the stonemasons because it did not seem to fit anywhere; but it was designed and ideally suited to bind all the angles of the building together.  Jesus also said that He was the rock of Daniel 2:34-35.  That rock was greater than every human authority and crushed all who stood in its way.  The religious leaders knew exactly what Jesus was saying but did not want to accept that He was their God.  So, although they would succeed in crucifying Him, He quoted the Scriptures prophesying that He would have the last word.
 
Keeping religious rules can never put us in favour with God, because we also break His rules: only 100% lifetime perfection could earn our place in His Kingdom.  But Jesus came to be punished for every impure thought, word and deed (Isaiah 53:5-6), so that we might be forgiven and be made righteous by His grace (see www.crosscheck.org.uk).  Jesus is therefore the touchstone of our eternal destiny.  Those who receive Him and allow Him to have His rightful place as Saviour and Lord - the One who holds all things together (Hebrews 1:3) - are welcomed into His Kingdom (John 1:12).  But those who treat Him as irrelevant to their lives will be crushed by Him.  And so, Jesus is the eternal testing stone.  That is why His people must proclaim His gospel and invite their friends and colleagues to receive God's love and forgiveness in Christ - anything less is a callous lack of compassion for those who will otherwise be crushed by the supreme authority of Jesus.