As much as I'd love to do that (and I seriously looked into trying to make it work), sadly the game engine simply doesn't allow for it. All images and animations are 2D, which means everything in them is "baked in" and can't be changed in realtime. I could make variation renders, but let's look at how that would work:
Let's say I keep things super simple and only have three skin colours, three hairstyles and three hair colours. That's still not enough for people to fully customise their character, and there would be complaints, but it results in the smallest amount of work for me (and bear in mind I'm a solo developer).
Now let's take each of the skin colours, hair styles and hair colours and call them A, B and C each. So someone using the first option for each would have the following variant image: AAA. Someone using the first option for skin colour and hair style, but the second option for hair colour would have the variant AAB.
And so on and so forth. You get it.
Now let's look at all of the possible combinations:
AAA
AAB
AAC
ABA
ABB
ABC
ACA
ACB
ACC
BAA
BAB
BAC
BBA
BBB
BBC
BCA
BCB
BCC
CAA
CAB
CAC
CBA
CBB
CBC
CCA
CCB
CCC
... whew! That's twenty-seven different, individual renders/animations that I would have to make for every single scene of every single event in which the main character appeared.
That means that every event with the MC in it would take twenty-seven times longer to make and would take up twenty-seven times as much space. And this is the bare minimum of work I would have to do, with options so limited that people would complain about them!
So, sadly, the answer is that CK will never have a customisable main character. My next game hopefully will, if I move off the Ren'py system, but for now you're stuck with the poor old pasty-white, mop-haired MC ;)