Characters are pretty important when writing fiction, and as the author, you often get very close to them - the number of times I've made myself cry over what's happened to my creations - but like an overprotective parent, you have to learn to give them their own space.
A particularly strong temptation is to project your own values, or those of your society onto your character or their society. Everyone wants their hero to be someone they would like, someone who they can see as 'good'. I know the pain of wanting my Roman legionary to be disgusted by gladiatorial games, my early modern European to be kind to animals, my tribe of barbarian warriors to treat men and women equally. It never works. Autre pays, autre moeurs - and the past is another country too, and unless you've set it in present day [fill in your country] a good person isn't usually your idea of a good person.
If your story is set in a real time period, try to make their morals fit. If it's a fictional place or period, resist the temptation to make them think like you, unless you're sure it fits. Try to work out what period it's most analogous to in terms of development: remember that it's no coincidence that times past were typically more violent, oppressive and xenophobic than today. Until you have the technology to make lives easy enough for people to have time and energy to spare, you don't have much time or energy to spare for looking after strangers. And just as you have to learn and develop from being a child to an adult, learning empathy, values, and that everyone is 'I', so societies have to develop, learning that other people are just as much people, that animals are sentient beings, that the Earth is not indestructible or inexhaustible.
Get this right, and you still have to decide how 'good' you want your heroes to be. It's up to you, but don't just make them saints because it's nicer that way. That's the easy way out and usually makes them insufferable. If you want them to be holier-than-thou, do it deliberately, as a character flaw. Let your heroes be flawed, unless you really think that a spotless angel is right for your story. It might be, but make sure it is. Otherwise give them dark secrets, murky pasts, chips on their shoulders and demons to face. Make them rounded, make them real, give them blackness in their hearts and let them be themselves.