A little flash that just occurred to me:
Protestants argue sola fide, that we are justified by faith alone. The Catholic position is often presented as fide et operis, by faith and works. But Catholics and Protestants agree that it is not our action or operation, either in having faith or doing works, that saves us, but entirely the grace of God (sola gratia).
The Apostle Paul writes in Ephesians 2:8-10:
For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.
Protestants get very hung up on the Catholic insistence on works, that works are necessary for salvation. But most Protestants admit this, if the question is posed the right way. As Saint James writes (James 2:14-17):
What good is it, my brothers, if someone says he has faith but does not have works? Can that faith save him? If a brother or sister is poorly clothed and lacking in daily food, and one of you says to them, ‘Go in peace, be warmed and filled,’ without giving them the things needed for the body, what good is that? So also faith by itself, if it does not have works, is dead.
As this makes evident, works are necessary. Faith without works is dead. Protestants argue from this that works follow faith — that true faith necessarily produces the fruit of good works; that if a brother does not produce good works, then he never had true faith to begin with. But the result is exactly the same: Good works are a necessary consequence of faith.
This is exactly what Catholics argue — only in affirming free will, Catholics present that it is incumbent upon the believer to choose to do good works, given the gift of God’s grace which enables the believer both to will and to work (Philippians 2:12-13).
Catholics affirm that our initial justification is by faith alone, as a gift of God’s grace, not because of any work or merit on our own. Protestants affirm that works are necessary for salvation — a necessary consequence of true faith. That puts the two parties on the same page regarding the necessity of both faith and works for salvation — and much closer to agreement than either would like to admit.