In Hamlet, what softens our realization that Hamlet is responsible for the deaths of Polonius, Ophelia, Laertes, Rosencratz, Guildentern, Claudius, and Gertrude?
Well, you could argue that Gertrude was more the result of the schemes of Claudius than Hamlet. You are right to lay the responsibility for the death of the other characters at Hamlet's door however. I suppose there are two ways of looking at this issue. One is to say that actually Hamlet is a very nasty, cold-hearted killer who deserves what he gets precisely because he shows himself to be more of a sinner than sinned against. In particular, this can be displayed through his coldhearted and manipulative murder of Rosencrantz and Guildenstern. They were really doing nothing wrong except obeying their King, and there was no need for Hamlet to have them executed. He could just have easily as left them alone and not changed the letter.
However, on the other hand, what we could argue softens Hamlet's crimes in this play is the fact that he is shown to be incredibly isolated and alone. Even those characters who he feels are his friends and he can trust seem to turn against him, such as Rosencrantz and Guildenstern. Even his lover, Ophelia, is shown to be used against him by her father and Claudius. Therefore we could see that his actions are the result of a particularly troubled individual who is desperately trying to make sense of his position in the world. In addition, let us remember that Horatio chooses to remember Hamlet in words that present him as a profoundly noble individual:
There are therefore two options in terms of your thinking about the character of Hamlet. He can either be viewed as a bad character or as a profoundly troubled individual. Your own thinking on this issue will impact what you think about his murders.