Its been a while for me on Christian Theology, but I'll chime in on this one. Its a good question and one that challenges the fairness and rationality of the theology behind how people are judged.
The key phrase to look for in theology is "Dispensation Theory".
On the question of whether people who don't have a chance to accept Christ automatically go to heaven - my understanding was that the answer to that is no. An automatic pass into heaven if you've never heard of Christ makes no sense at all as you have pointed out. According to the theology that I am familiar with, how they are judged depends on when they lived and what circumstances they were in. If they lived before Moses' Laws, then they are in the so called "Dispensation of Concience". The same criteria goes for non-Jewish people (called Gentiles by Paul)who have never heard about Christ Here's a quote ...
Romans 2:14-15, " For when Gentiles who do not have the Law do instinctively the things of the Law, these, not having the Law, are a law to themselves, in that they show the work of the Law written in their hearts, their conscience bearing witness and their thoughts alternately accusing or else defending them,"
Now if you are Jewish before Christ - then you are under the Mosaic Law (Dispensation of Law).
And there are other dispensations that cover other categories.
Now I am not sure how widely dispensation theory is accepted by different denominations - which ones believe it or which get outraged by it.
I've never been a fan of the tendancy of some denominations to emphasise converting people and crusading above all else. So I've asked these kinds of questions too.