First of all, I would ignore Protestant interpretations of scripture.
I can, however, offer a traditional Orthodox explanation that was taught to me.
The reason for the closed doors to the altar is to symbolize that sin has cut us away from Holiness.
In another sense, it is to remind us that there are mysteries in this world which we do not understand and can not witness.
Protestants, I would imagine, would quarrel with the first interpretation, as they seem to believe that once you claim Jesus as your saviour, you are automatically saved, regardless of sin. In fact, I have had discussions with Protestants who claim that sin can't keep you from being saved because of some proof text that says everyone who accepts Jesus as saviour is automatically savedand that not believing that promise of scripture (salvation) is blasphemous.
I am not the best authority on Protestantism, but I am pretty sure that in Orthodoxy, the closed gates are a symbolic representation of man's distance from God caused by sin, and that the opening of the Royal Gates when the chalice is brought out represents the coming of Christ to overcome that sin.
This is what I was taught by Abp Anthony of San Francisco of blessed memory.