In your opinion, how hard should one strive to be good? Actually, I think that this question sort of starts in the middle it that it assumes a number of things (e.g. whether there is any such thing as good) and it leaves a number of others unanswered (e.g. what is good). What do you think, leaving the assumptions and unanswered questions alone for now? I suppose you may find my question silly from a strictly atheistic perspective. Oh well, indulge me if you will.
I do think it's important to be good and to strive to always be good without exception. The reason is that being good and living in alignment with your conscience promotes well being. It dissolves guilt, fosters self-connection, and infuses people with meaning. Since those things are generally thought desirable, it makes sense to take steps to develop them.
Would I say that others have a responsibility to be good? I wouldn't, because I don't think philosophies can ever give rise to ethical systems and the values they depend on. Those values come from contemplation, wisdom, and appreciation (or some other moral authority).
The harder question is how to define good, but I think it's something that needs to come from a person's core, rather than via authority.