Here is a complete picture list with all the RARE dyes currently in the game, including a selection of uncommon ones that are hard to get. My main char was patient enough to pose for a screenshot of each dye
I made this post to help players who might be after a certain dye, but don't know exactly how it looks, or if it is worth the effort, because as you will see, many dyes are very similar.
I know this is not perfect, nor it can be, because how dyes look depends a lot on the costume/outfit.
So I picked "Drifting Sand" Tunic and Sash because of simplicity. It does not change the hue much, does not make the colors to dull or shiny, and has parts with different level of shine. The thin sash is the most shiny part of this costume, and it has the same shine like a metal pieces of armor. I used an outfit station placed inside, with an Alinor lantern nearby, to have a neutral to warm lightsource, for "shiny" colors. Screenshots were taken during game night time, so other lighting condition won't affect the setup (I don't know exactly to what degree the outfit station resets lighting, but wanted to be on the safe side). In the begining I wanted to post only material crops instead of showing my char, but I think it is better to see the whole costume in order to properly evaluate the dye.
Rare dyes:
Abyssal Beryl
Adamantine Silver
Aetherial Blue
Akatosh Scales Gold
Arcane Blue
Atmoran Bronze
Aurora Green
Ayleid Gold
Bedlam Purple
Blademaster's Mauve
Bloodroot Wine
Celestial Violet
Coldhabour Black
Colossus Brass
Contraband Violet
Covenant Blue
Cyrodiilic Steel
Daedric Red
Divine Gold
Dominion Yellow
Dragonstar Red
Dwarven Brass
Enteloma Blue
Epic Violet
General's Gold
Grand Overlord's Brass
Grand Warlord's Violet
Indomitable Violet
Julianos White
Lamae White
Legate's Black
Liar's Linen
Lycanthrope Grey
Magnus Setting Red
Motif Master Brown
Mundus Blue
Nacreous Purple
Necromancer Blue
Nirncrux Red
Nirnroot Gray
Ophidian Jade
Orhicalc Green
Overlord's Purple
Pact Blood Red
Palatine's White
Putrid Flesh Teal
Ruby Throne Red
Scalecourt Brown
Sigil Orange
Slaughterfish Pink
Stalhrim Chrome (Wolfhunter DLC)
Superior Blue
Syffim Red
Transliminal Violet
Undaunted Bronze
Vekh's Mystic Blue
Viridian Venom
Voidstone Violet
Warlord's Red
Warrior's Steel
Uncommon "rare" dyes:
Antique Silver
Covenant Fisher Blue
Dominion Fisher Yellow
Pact Fisher Red
Regicide Red
Shrike Blue (Summerset completionist)
Stendarr White
Polished Steel
From my experience, the most desired basic colors in this type of game are white, black, and metallic colors to dye weapons, armors, and other outfit elements. Shiny brass-gold is quite desired. Some of these are hard to get, other not so difficult. One big surprise is the Rank 5 material black, which is quite good for a very easy to obtain dye (deconstructing mats). Other very hard to get dyes are a let down, but you be the judge of that. From my experience, Liar's linen is great for silver lining, or steel-like weapons and metals, and Transliminal Violet the best for gold insertions.
Julianos White remains the brightest best white, but Palatine's White is also great (Julianos has a slight blue tint, Palatine's has a warm pink tint).
Below is a comparison chart for these dyes. I might update it with crops taken from a shield or armor for metallic colors.
I hope you will find this useful, and if you have ideas how to make this better, please comment below.