First, let me say that I do not write to proselytize, merely to proffer some thoughts on your post.
Second, while you may, to a large extent, have been surrounded by people who strove to be good, this is not the lot of all of humanity. Stalin, Hitler, ISIS that chooses to terrorize fellow Muslims, rather than seize opportunity for emancipation of people, and al Qaeda all are realities of life.
Clearly, an organization that blows up people of the same Muslim faith in order to make a political point cannot be deemed to be good.
While morality is, absent belief in God within reach of man, it takes only a cursory look around to arrive at the realization that there are more who struggle with morality, than live up to it.
Third, it is not true that Christians believe only those who have faith in Jesus Christ have capacity for morality. Just so you know I am not attempting to blow smoke, as such attempting to retreat after the fact (of your post), here is a link to a Medium post that I wrote on self same subject more than a year ago.
Whether a person is a Christian or not, Christian beliefs declare that he or she is rewarded by God on basis of his or her actions. You see then, that, in so far as morality is concerned, that there is not any exclusionary wall in Christianity.
If any Christians seem to state existence of such a ‘reward-non-reward’ wall for good actions, they do so out of some ignorance.
Fourth, as to rationality of faith in Jesus Christ, this is about relationship with God, not morality. Jesus did not come to earth so we are able to be moral, He came to earth to create the opportunity for acquiring His nature, for acquiring the nature of God.
You will agree with me that if Jesus and His Father truly are who they claim to be, that it is far better to have their nature than to hold on to the Adamic nature.
Right there and then is where the rubber meets the road, the point at which each person has to either ignore the possibility, or attempt, on basis of the available evidence, to arrive at a personal decision. Personally, I have found the leap of faith that bridges the evidence and the resurrection of Jesus Christ — which no one can prove for a fact to be true or untrue — to be no more than I can demand from my reasonableness.