Mat 10:16 “Behold, I send you out as sheep in the midst of wolves. Therefore be wise as serpents and harmless as doves”

Both are required. If you are displaying street smartness using the wisdom of men, then you can not be harmless as doves. Because at some point your action will hurt, trump or affect some one else life. In this Abraham and Abimelech incident, it affected Abimelech. Their ladies can not give birth. Abimelech was about to sin and die. Many things will be affected in men’s life if we use this ‘Wise as Serpents’ terminology to match with wisdom of men.
If we see in the scriptures harmless is associated with the surrounding in which we are living in (Phil 2:15, Heb 7:26). Our Lord is sending the disciples into the midst of wolves and/or perverse generations. If they are not using the wisdom of God, then they would be torn by the wolves or consumed by the perverse group. They have to use the leading of the Holy Spirit to live a life like Christ when He was in the world in the flesh. He was separate from sinners and undefiled (Heb 7:26). At the same time, He also moved with His fold harmless, whether they are sinners or righteous. Separate with sinners and dined with sinners? Why it is contradictory in the life of Christ? It is not contradictory, but it is how God see from His viewpoint. Whom men classify as ‘Sinners’ may not be a sinner in God’s view point; they are just a lost sheep. Whom, men classify as ‘Saints’ may be wolves or worst sinners in God’s view point. To see from God’s viewpoint we have to use His wisdom. Worldly wisdom cannot see as God sees. Abraham wanted to be careful among the ungodly people or perverse generation, but forgot to see or not able to see a neighbor. Be wise as serpents among the wolves, and harmless as doves among the sheep. That is true wisdom and true love.