15 Dec 2019 - I decided to rewrite this patcher into a new mod, you can find it here

Hair Patcher Two
Personally I prefer the new one, but feel free to use what you prefer

24/03/2017 - Uploaded JIP NVSE version.
03/07/2016 - It was reported an incompatibility with the Beta of Lutana. If you want to use this mod please install the main Lutana version.
10/06/2016 - If you want to update to 1.0, please do a clean save
21/03/2016 - Updated 0.9 - PLEASE DO A CLEAN SAVE

Description
Everytime you install custom hairs or custom eyes, if you want them to be used in your favourite custom race you must open the GECK and add them in the list - basically you must patch them manually.
 
This small script tries to do it, automatically.
 
You'll be able to load any hairstyle and eyes, and it will spread it on any race you have installed. Il will execute when you load the game, when you'll arrive in the main menu - the game will freeze when loading the arrays, and when it has finished it will show you a message box. NOTE: if you'll open the console at this point, you'll be able to see how many eyes / hairs were added to records.
If you have slowdowns / freezes after the message box, they're not caused by this mod. How much time it will take to load the records? it varies by some factors. It makes many operations, it can make *some thousand* operations. I tried with ARES + Mojave Delight + Mojave Delighted + Mikoto, it took about 4 seconds to load everything. Considering how big Mikoto is, it was a very fine result for me. If your loading times are too high, then consider to reduce the number of races / hairs or not use this small mod.
 
The mod also provides you two items under Apparel, named [Mirror-Hairs] and [Mirror-Eyes]. If you click on them, it will close the pipboy and after 1-2 seconds it will open the barber menu for hairs and the plastic surgeon menu for eyes, so you'll be able to change your hairstyle.
 
Requisites
NVSE 5+
JIP NVSE
 
Installation
Drop the ESP under Data and activate it. To uninstall, simply remove it and make a clean save.
 
Issues and Conflicts
16/03 - I found a possible issue, please read the part in red.

For hairs, maybe you could have some improper hairstyles if you play with child races, it's not made for child races. If you find any issues please use the thread to warn me.

A note about eyes: there are some mods that introduce a new kind of eye, with a different UV. Basically, its texture can't be adapted over a vanilla eye and vice-versa. Translated in practical terms, it means that since this mod knows nothing about which model you install and it only merges them all together, you'll find yourself with some eyes that look well and some other eyes that have obviously a wrong texture over them. You can't do anything about it. To use a fantasy comparison, it's like if you install UNP body on Skyrim and then you want to use CBBE textures over it.

There are essentially a couple of things to consider, I found them during my tests.

- One is well known since always, you can read about it on some race pages too (i.e. Mojave Delight if I remember well). It is about the fact that under some circumstances you can't change eyes and hairs together. If you want to change eyes, you should first choose some vanilla hair and then change eyes and then change hair back to your custom model. I say "under some circumstances" because for Mojave Delight and its eyes / hairs it always happened to me, but on other races it doesn't, so I still can't say what's the real cause.

- The second is a lil more strange. It's still about eyes, they cause me random freezes if I change them on the fly in game. As it is, it seems game engine related, and it depends by the kind of custom race I'm using. For example, with vanilla race and custom eyes + hairs I didnt' have problems, while on ARES I had it often.

This, for me, means that you probably will be able to use every hair and eye you want (but keep in mind the point number One for some races) during the character creation, but changing them later could lead to problems, so save your game before changing something to avoid to loose where you arrived, because of the freeze. This also means that you probably could avoid further freezes if you swap race, but it causes other downsides, in every Bethesda game changing race resets things like attributes / skills etc.

TL;DR THERE SHOULDN'T BE ISSUES DURING CHARACTER'S CREATION, BUT THERE COULD BE SOME IF CHANGING THE ASPECT LATER. I'LL LEAVE THE TWO MIRRORS ON THE PLAYER'S INVENTORY, BUT BEFORE SWAPPING YOUR ASPECT ON THE FLY (mainly eyes), PLEASE MAKE A SAVE FIRST.

Also, it could be that some mods like NVAC or some specific tweaks / settings could reduce or avoid this issue, it could be nice to make further tests with these.

 
Credits
hlp for NVSE 4+
Luthien Anarion for Lutana
raschau for the idea of adding eyes
 
Permissions
My general rule on permissions - you can do whatever you want but not for commercial use; if it's marked as Beta/WIP, then do not use it, it's better if you contact me and we cooperate; if you use something from my mods, some credit would be nice, but if you can please inherit the permissions, so that others will be able to use your mod too, mods deserve to be spreaded.