Protestants generally agree that Salvation is by faith alone but Christians disagree over what constitutes faith which is important because that is the means by which we are saved.
One view is that the Greek word translated to faith (pistis) has a wide variety of meaning in the NT and is sometimes translated as "faithfulness" depending on the context. Matthew Bates in "Salvation by Allegiance" alone contends that "pistis" should be understood as "allegiance" which encompasses mental agreement, fidelity, loyalty, etc. He cites as an example, a Jewish rebel who wrote a letter urging people to "repent and believe [pistis] in him" as means to join his cause, using the same language as the New Testament Greek during the same time period. [
https://thelogosofagape.wordpress.co...ek-word-study/]
Another view is that faith is both mental agreement and trust and that obedience is a fruit of faith. This view is held by theologians like Wayne Grudem (see [
https://www.youtube.com/watch?v=Ujtk2ZGzHkw]). Notice in John 3:36 that obedience and belief are almost used interchangeably perhaps because they are so closely interconnected.
John 3:36
Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him.
Acts 5:32
And we are witnesses to these things, and so is the Holy Spirit, whom God has given to those who obey him.
Another view closer to LCs is that faith is just mental agreement alone. I agree mental agreement to the correct divine facts is important. For example if I mentally agree that Jesus was a created being, the archangel Michael and that he was a spirit being who never died but only ascended to heaven, that kind of Jesus will not save me.
Two examples in the OT provide an interesting case study: David and Balaam. Both mentally agreed that Yahweh was God but only David directed his allegiance/love/obedience towards God whereas Balaam was really loyal to himself and money. David murdered, stole, lied and committed adultery yet he was ultimately saved. Balaam may have not committed such sins and was even used by God to prophesy and speak truth but he was disobedient in his heart and he was ultimately damned according to 2 Peter 2.
I think there is some wisdom to focusing on faith even if it is just to increase one's level of mental agreement. I found the more I research about the veracity and trustworthiness of the bible which helps me to be fully convinced of the gospel, the more I am able to become obedient with little effort. I find that the more I believe, the more God puts desires in my heart to do his will and to love the things he loves and hate the things he hates. In the past I focused on good works or overcoming addiction by my own effort without focusing on developing faith and it often failed. Perhaps the Holy Spirit is able to work through us according to the measure of our faith.
1 John 5:4 ESV
For everyone who has been born of God overcomes the world. And this is the victory that has overcome the world—our faith.