How do you integrate your morally pure characters into Skyrim's society without killing someone?

Sleep in the Temple of Kynareth and spend your days healing the soldiers?

That will be a problem if you venture anywhere outside of a city...the first time a bandit corners you it will be over for your "milk drinker" character.

It will take some quick foot work... but the spells: Calm. Paralyze & Invisibility. ...muffle would help.

but on PC you could also used console commands to make it so that nothing would attack....that your PC is in the "friend" faction for everything basically. Their is a mod that would work for animals and their may be something that can be found for all the hostile npc's.

I have played a few of characters in TES who didn't kill anything (creatures or humanoids). They all did a whole lot of running. (Fortunately, this is easier in Skyrim than it was in Oblivion where enemies would relentlessly follow you, Terminator-like, across the entirety of Cyrodiil). In addition to the spells mentioned, Sneak can also help out a lot.

My only Skyrim pacifist so far has been a Miner. She was strong enough to fight, but chose not to. She spent her game traveling from node to node, collecting ore, sometimes smelting it, then selling raw materials to Smiths in various cities. She knew from extensive travels where most of the dangerous spots were and avoided them. When she inadvertently attracted hostile attention, she ran.

Edit: Just had a thought - you could grab a deserted location (like the Alchemist Shed in Riften) and squat there. That's not bad, no obligations to the local Jarl and you could hunt and mine to your heart's content. That's the answer for a 'no houses, no titles' playthrough. The rest of my post is probably not what you're looking for, but FYI:

/Edit

So ... morally pure... does that mean your character won't help a village that's being attacked by vampires? How about a Daedra? It's one thing to slaughter everything you come across just because it's possible, but it's not much better to turn away from those that need help...

I think I'd opt for a middle ground - let's say you stall the MQ and never venture much beyond the main cities. You'd be looking for a place to settle in the country so you can farm. You'd need a Hearthfire house (maybe Winstad - you can farm and fish?) so which one is the least morally-challenging to acquire?

• Lakeview Manor. forget it! The Jarl requires that you go kill his criminal partners before letting you buy land.
• Heljarchen Hall - nope, you save the people of Dawnstar from a Daedra (yay!) but then you have to kill some poor giant just to send a 'message'
• Windstad Manor - probably the only choice. Save the people of Morthal from a vampire coven and do some relatively innocuous favors and you've got a homested.

Now, what if you don't want to farm? Maybe you'll just hunt? Then you can buy a city house but not before becoming Thane. There's some bloody work ahead...

I've played really, really good characters in Skyrim whose purpose was to help those in need and you can do it, the game does support that persona, but it doesn't mean you won't have to fight.

Good luck - let us know what you decide to do and how it turns out. I kind of like the idea of a hunter/craftsman build who lives in a city and makes a living from the surrounding countryside... gotta think about that...

On PC the mod "homes for everyone " let's you buy any of the houses without all the rig-a-ma-roll...still gotta have the money. And If I Remember The Read me right, It's Still suggested to do Blood on the Ice, if you plan on doing the civil war.

But it would allow a moral character to buy any of the HF houses.... of course one can just use a mod house that requires no effort... up to them.

On PC, the mod Campfire gives you the ability to set up camp anywhere. If you are not so pacifist that you won't hunt, then you can hunt game for food and selling. This works really well in tandem with the Hunterborn mod. You could even set up shop away from the cities, and still have good trade partners, if you set up somewhere along the route of a Khajiit travel caravan.

Or you can forage for food and materials otherwise. With a little scouting, you could find a relatively safe location to set up your camp/home, close enough to material resources to sell and to a town to sell them to.

Otherwise, as others have mentioned, something like the alchemist shack to live in, and the spells and running already mentioned.

Or, you could just go work in a lumber mill, or do smithing work for the woman imperial smith in Whiterun, or something like that. Not sure how much interesting gameplay would come from that though...