Is there evidence in Hamlet's soliloquy, 'To be or not to be' that supports his desire to protect his kingdom from Claudius and Gertrude?
This is an interesting concept to consider, but I have to say that I certainly do not see any such assurances in this soliloquy. Let us remember that in this speech Hamlet is trying to work out whether it would be better for him to commit suicide to escape the woes that he is experiencing or to try and surive the "slings and arrows of outrageous fortune." This is essentially a very selfish speech, and this is definitely one of the criticisms that we can level against Hamlet. In the play he seems to show little care for the kingdom that by rights he should have inherited. What concerns him more is his own feelings and the memory of his father. This speech is a profoundly selfish speech as it focuses on Hamlet's feelings alone and his own attempt to try and work out what to do.
Therefore I don't think we can find any evidence in this speech to suggest Hamlet cares about anything else than himself and his own troubles. This is a very self-centred speech, and it helps us to understand the various questions that plague Hamlet about his life and its value.