It is as though the Christian God, for example, is saying:
"I am an all loving and all just God. I have had my son sacrificed. So in order for people to be convinced of my existence and of my son's sacrifice, I will just throw some things out there. Namely, the bible that I know many honest open minded people will not be convinced of. But if they still don't believe, then that is just too bad.
Especially for little children who die early and other people in other areas of the world who never got the chance to believe in me. I will not try to convince them any more than this even though I am an all powerful God who is more than capable of trying to do so. So that is all I am going to offer as a means of conviction. So take it or leave it. If you are not convinced and end up in hell, then that is just too bad and I am just going to have to leave you there to suffer for eternity."
So don't you see how such an attitude is not all loving, not all caring/just, and not morally righteous?
You apparently misunderstood the situation. It's only logical when a judgment being made based on a correct understanding of the situation.
It is said that God has an Ultimate Plan, which is to build an eternity (we called heaven) for His creatures to live with Him forever. To facilitate this plan, the first thing to do is to specify a set a Law which states God's likes and dislikes such that those qualified to be living in Heaven must not break the Law. It's more like you have some guests in your house who would stay for several months and you set up some rules for them to follow in order to live in peace with you.
Then Adam broke the Law and thus is disqualified. Adam was then driven out of God's realm (i.e., Eden). Once living outside God's realm and put under the deeper influence of Satan, no humans can abide by God's set of Law to be qualified. That is, if someone is as innocent and good as Adam can't resist Satan temptation but breaks God's Law even inside God's own place, then it is expected no one can resist Satan's influence when put outside God's realm. That is, humans as a whole have no hope of entering heaven.
However, Jesus made a decision, as part of God's Plan, to sacrifice Himself to justify the situation. With Jesus' this decision made, it makes possible for God to establish a series of covenants to the different human groups in different eras. A covenant simply says that, "since you humans can't abide by God's Law in full, you only need to abide by a set-aside set of rules (such as Mosaic Law) to a said standard, such that you will be saved by God's Grace through Jesus Christ."
Every human is born with a default covenant to make him savable at all. However, as time goes by, a covenant may lose its salvation power because humans keep walking farther and farther away from God. They become more sinful for the existing covenant to save. Thus God will introduce a newer covenant to re-acquire the salvation power. In a nutshell, each and every covenant serves the main purpose of identifying and thus separating the righteous from the wicked. The righteous thus will be brought to Heaven legitimately under open witnessing (of angels and chosen saints).
Then Jesus came and brought humans with the last and final covenant. In this covenant, God's Grace is maximized such that humans only need to put faith in Jesus/God to be saved (i.e., Law, such as Mosaic Law, is no longer used as a standard to judge who are the righteous).
If you have no faith in Christ, it means that you failed to choose the New Covenant as your protection. You are then subject to an older covenant with which you were born. You have not much hope to be saved with this older covenant as warned by the Bible.
On the other hand, a covenant is like a gift not earned by humans but by the self-sacrifice of God and Christ. God and Christ thus have all the right to grant it to whoever they'd like to. There's no unfairness here. All left is the effort of humans to preach the gospel for this gift to reach other humans for them to make a choice.
That's the situation.