Most controversial passages

Doctrinal disputes that have split churches

• Matthew 16:18, "on this rock I will build my church." Catholics read it as establishing Peter's primacy, Orthodox tend to read it as pointing to Peter's confession, and many Protestants read it as pointing to Christ himself. A lot of church history hangs on this verse.
• "This is my body" (Matthew 26:26 and parallels, plus John 6). Transubstantiation, consubstantiation, spiritual presence, and memorial views all grow from how this is read.
• Romans 9, on God choosing Jacob over Esau and having mercy on whom he wills. It's central to the Calvinist and Arminian divide over predestination and free will.
• Romans 3:28 and James 2:24. Paul says people are justified by faith apart from works, while James says a person is justified by works and not by faith alone. Reconciling them shaped the Reformation debates.

Passages contested over ethics and practice

• 1 Timothy 2:12 and 1 Corinthians 14:34-35, on women teaching or speaking in church, which divide complementarians and egalitarians.
• Romans 1:26-27, Leviticus 18:22, and 1 Corinthians 6:9, on same-sex relationships. This is probably the most publicly contentious area today.
• Matthew 19:9, on divorce and remarriage.

Passages that trouble readers on moral grounds

• The Canaanite conquest passages (Deuteronomy 20, Joshua 6-11), where God commands the destruction of whole peoples.
• Genesis 22, the binding of Isaac, and Psalm 137:9, which ends with a wish to dash infants against rocks.

If I had to pick one by sheer scale of historical impact, I'd say Matthew 16:18. For the strongest ongoing public controversy, it would be the passages on sexuality, and for the hardest moral questions, the conquest narratives.