The FCS made this incredibly easy, it was as simple as: right click on eg Armoured Rags (colored) -> "Replace References" -> Armoured Rags

This way the FCS replaces all instances of Armoured Rags (colored) with the regular Armoured Rags, and all I had to do was go back and set the base item to be colorizable (and make sure there really weren't any other differences between the two)

What does this accomplish? 
Well it means that you should see a bit more faction color on any random NPC, if you want to enhance the effect then I recommend:
Faction Armor Colors - Better Colormaps - and maybe even try out the other mod I made for it (linked in that mod's comment section)

I did this for:
Armoured Rag Skirt (colored)
Armoured Rags (colored)
Cargopants (colored)
Dyed Rag Shirt
Dyed Turban
Dyed Turtleneck
Halfpants (colored)
Rag Loincloth (dyed)
Stout Hessian

Now the prickly part... I'd LIKE to remove these items completely from the game, but that would not play well with other mods and be a compatibility nightmare.  Thus, I left the base items in while letting FCS remove any references to the item from any other source in the base game.  This *should* make it safe to install mid-playthrough without needing to import since any already existing items will remain, and the mod just removes any future instances from spawning.  That should also mean that other mods will be able to add new references to the "removed" items without breaking, but those mods would then be the only source of these removed items in your game going forward, not perfect but I think this is the best possible solution.  If you wanted to remove the mod references too, you could repeat my steps with all your mods loaded... this could probably be automated with a script, but I don't know how to make one of those - sorry.
I did make patches for the mods I use (available in the optional downloads section) not using them won't break anything, they just remove references added by those mods to these items too.

There were some edge cases which I considered including here but I'm not yet sold on - post your thoughts on these in the comment section!

• Bandana / Black Bandana / Red Bandana and similar such items - I ended up leaving these alone since the base item is colorizable and the alternate versions are specific colors, I did consider standardizing the names to eg "Bandana (Red)" but then I'd want to standardize ALL Kenshi item naming conventions and... let's not open that can of worms...
• Dyed Robes / Trousers - these follow in the same vein as the other items, so why not these?  Well, there is no great substitute for these specific ones since they are used to dress slaves and the available alternatives of eg Monk's Robes or Noble's Robes feel out of place... so I left them as an exception.
• Empire Samurai Armour - This is the closest edge case I came to including, but during my investigation I discovered that the devs snuck in a change to these in some recent patch - they now provide 0.5x Dodge mult instead of the usual 0.6x.  Plus, according to the description, this version includes a UC emblem on it... I can't say that I see it... but I'll take the wiki's word for it.
• Plate Jacket - to make this item colorizable I'd have to remove it's current color... which would make it indistinguishable from a White Plate Jacket until it was dyed... not ideal... I could make the White Plate Jacket colorizable... but then it wouldn't be white... hmmm...  Best I could do would be to rename the base item eg Grey Plate Jacket and make the White one the base/dye-able version, but I don't love that either...
  

If you think I missed something, do let me know!