I think we all agree that we need faith in order to be saved. Let's focus on obedience.
Is obedience a second condition for our salvation. In other words, do we need both faith and obedience in order to be saved?
Or is obedience the natural result and outworking of genuine faith? In other words, when "faith" is properly understood, is it simply redundant to tack on obedience as a condition for salvation?
To ask the same question in another way - are faith and obedience two different things or are they really two ways of looking at the same thing? Can true faith exist without obedience? Can obedience exist without true faith?
My contention is that we are saved by faith alone. But "faith", properly understood, is an active faith which works itself out in loving obedience.
While it is true that Abraham believed God, so he was justified, it is also true that Abraham believed God, so he obeyed God's command to offer Isaac, so he was justified by faith and obeyed by the same faith, but he was not justified by his obedience. In Matthew 23:23, Jesus said that faith is one of the weightier matters of the Law, so obedience to God should always be considered to be acting in faith. Every example of someone living by faith in the Bible is also an example of someone living in obedience to God's will, such as the examples of faith listed in Hebrews 11, whereas disobedience to God's Law is referred to as breaking faith, such as in Numbers 5:6. In James 2:17-18, he said that faith without works is dead and that he would show his faith by his works, so obedience to God is what faith looks like. Obedience to any set of instructions is about putting our faith in the one who gave them to correctly guide us, so only those who has faith in God to guide us will obey His Law and be justified by that same faith, which is why Paul said in Romans 2:13 that only doers of the Law will be justified.
To use an analogy, if a professional musician were to teach me how to play an instrument as a free gift to me, then their teaching would be the content of the gift and participating in this training would not be doing anything to earn their gift, but rather it is what it would look like to receive their gift.
In the same way, in Titus 2:11-14, our salvation is described as being trained by grace to do what is godly, righteous, and good, and to renounce doing what is ungodly, which is essentially what God's Law was given to instruct how to do. Furthermore, it says that Jesus gave himself to redeem us from all Lawlessness and to purify for himself a people of his own possession who are zealous for doing good works, being redeemed from our Lawlessness and being training to do good works in obedience to God's Law is the content of the gift of salvation. Participating in this training would not be doing anything to earn the gift, but rather it is what it looks like to receive the gift. Our salvation is from sin (Matthew 1:21) and sin is defined as the transgression of God's Law (1 John 3:4), so being trained by grace to live in obedience to God's Law through faith is what being saved from living in disobedience to God's Law looks like.
Faith can exist without obedience when someone is physically prevented from expressing their faith, such as with the thief on the cross, but if our arms and feet aren't nailed to a cross, then we don't have that excuse. Someone can give the outward appearance of obedience apart from faith in Christ, but they would be missing the point, which is why Paul considered that to be rubbish.