Why would God care more about what we believe about God than how we live for God?
The first point I would make is that "believe" and "faith" in the Bible is primary about trusting God and his faithfulness. This is also why we fundamentalists emphasise the reliability of the Bible as God's Word - God is faithful and trustworthy, also in his communication with us (i.e. his inspired Word), otherwise how could we trust Him?
But the real answer to the actual question is this: What we truly believe determines how we live and how we act. If we do not trust Him, we cannot truly love Him. We cannot live a life of dependence on Him. We cannot truly love even our enemies, because He loves them. We cannot look at the world through His eyes. We can try do do all of these things as "followers" of Jesus Christ (Christians), but what will inevitably happens, is that we will eventually discover (even if it takes years) that this is simply not humanly possible (without supernatural help). And when that happens, we can react to this realisation in a number of different ways (all bad), unless we have learned to believe in Him:
- We give up on the Christian life and on the Christian message. We become either a New Age "spiritual person" believing that all religions are basically the same and only accepting the "ethical teachings" from each (according to our own definition of "ethical" now) OR we become atheist agnostic. We basically concludes that "Christianity doesn't work".
- We redefines who God is and what He expects of us according to how we want Him to be. So we choose our ethics of love according to what we find easy and possible for ourselves. Those sins of which we are not guilty, we condemn (especially lack of love in others), while we excuse the sins of which we are guilty as acceptable to God (through various creative reinterpretations) because "He loves us". We basically redefine "Christianity" to suit ourselves, creating an idol of our own making.
James 2 makes the point clearly that what we truly believe, determines how we act, irrespective of what we say we believe. If I believe the Good News as proclaimed in the Bible about God's breaking into our world through his Son, Jesus of Nazareth, it will change my life. If however, I only see Jesus as a good teacher (as did many of the Pharisees if his day), it will simply set me up for failure in trying to attain the high standards of his Kingdom. I cannot follow Him if I did not do a proper cost analysis (Luk.14). And part of that analysis involves the level of trust I am prepared to give to Him. And this is why I believe that it matters more to God what we believe (what is going on in our hearts) than how we live (what we do outwardly). Jesus repeatedly taught that it matters more that we actually clean the inside (which only He can do!) than that we appear clean from the outside. Of course, if nothing happens on the outside, it is evidence that we do not truly believe in Him, but only say that we do.