Do mudguards/fenders help? If so, what are the best for a fixie commuter?
I have a pair of SKS Race Blades (e.g. from Wiggle). They clip on and off really easily, for washing, security or just for the long days of summer when rain is decidedly unlikely. They are reasonably small and should fit all but the tightest of clearances. 

For all the reasons you mention, I use them - cleanliness of my legs, back, bag and chain - but also because I like to at least play at being a good citizen. On my commute there are lots of other cyclists. Would you prefer to ride in the wet behind someone with or without guards? So the fact I'm being nice to my fellow cyclists is a really cool side benefit. 

And if you think mudguards are sacrilege then, to be honest, you're probably not going to be reading this; style-over-substance hipsters are only dimly aware of the real reasons for cycling, only doing it because they think it's cool. And while it is cool, only not for the reasons they think ...