After a bunch of searching, it seems to me that there's no way to move without potentially accidentally attacking champions. It seems asinine to me that such basic functionality doesn't exist especially in a game where positioning is like the single most important aspect. What are the chances of Riot adding this? Is a place to petition for such a thing?
Just for thoroughness:
"Target Champions Only" toggle
Obviously doesn't work if you're trying to walk around a champion
Disable "auto-attack" in game options
This only makes it so your champ won't automatically try to basic attack enemies you hit with an ability
Hold down right click
You'll still attack anyone your mouse hovers over before releasing the click
Aim "wide"
Not always an option, there can be walls, etc. that would make your character walk in a completely different direction than you want
That's the "wide" solution and doesn't always work. Beyond that, even if it did work it would be suboptimal. I come from a domain of games where not letting your players be precise is a grave sin and capital offense. So this just seems unbelievable.
What exactly are you trying to solve? What about League isn't precise?
You're coming in pretty hot for a piece of functionality that doesn't make sense/is unnecessary the way you described it.