I've seen quite a lot of people listing markings and traits that are not Breed Only (BO) as Breed Only and it causes a lot of confusion among players, so I decided to make a little list of what is and isn't BO to help avoid confusion.

It's a long post, so use ctrl+f to look for colors/marking/mane type with single word (ex. Feline OR Orchid OR Savage). If it's not listed under BO - it is NOT BO.

Bases:

Breed-Only bases cannot be applied using Base Changers or any other applicators. They can only be achieved via breeding.

The special genetics bases are:

NCL exclusive bases
Asali, Dhahabi, Maziwa, Mobola

Weekly Raffle Lioness bases
Bushveld, Haze, Lilac, Orchid, Pearl, Pecora and Sepia

May Groupies bases
Abyssinian, Damu, Nudar, Ripe, Sahara, Sunspot, and Wine

July Raffle Lionesses bases
Celestial, Dawn, Jellyfish, Leonid, Prismatic, Sidereal, Skyward, Stratosphere, Sunrise, and Sunset

August Studs bases
Bandit, Outlaw, Ruffian, Scoundrel, Ukame, and Vagabond

Hybrid bases
Kimanjano and Mandarin

The rare genetics bases are listed here on wiki.

Combo bases are also Breed Only.
Bases that are used for combo breeding and are FROM APPLICATORS are NOT Breed Only.


Now let's talk Markings.

Tier 0 - Common Markings - markings that show up on NCL's - they can be obtained via the Marking Applicator in the Oasis, the Oasis Customiser tools, Random Marking Applicators, and Total Shuffles. This makes them NOT breed only.

Tier 1 - Custom Markings - markings you can apply with specific items - via the Marking Applicator in the Oasis, the Oasis Customiser tools, Random Marking Applicators, and Total Shuffles. This makes them NOT breed only.

Tier 2 - Raffle Markings - Also known as "Breed-Only Markings" or "Special Markings", these markings originate from raffle lionesses released each week. They cannot be selectively applied and must only be bred down from parents with the markings or randomly obtained with luck from Random Marking Applicators and Total Shuffles. This way of obtaining them means they ARE breed only. (0.5% chance to get it from RMA/Total Shuffle)

Tier 3 - Event Markings - These markings include April, February, and September event-exclusive NCL markings, July and August event exclusive markings, exclusive NCL markings (Cinnabar, Clay, Copal, and Marigold), and event applicator markings—basically anything that originates from an event can be found in this tier! Some of these markings cannot be selectively applied, while others can. They can be randomly obtained with luck from Random Marking Applicators and Total Shuffles. This makes SOME of them Breed Only.

List of breed only T3 markings that CANNOT be applied in November via Piety (the non-ncl event markings):

July Celestial Raffle Markings

Celestial
Agouti, Cover, Shine, Speckles

Dawn
Dapple, Lace, Margay, Shine

Leonid
Coat, Feline, Smoke, Undershine

Prismatic
Feline, Glaze, Smoke, Undercover

Sidereal
Cover, Glaze, Points, Shine

Skyward
Cover, Crumbing, Shine, Undercover

Stratosphere
Feline, Lycaon, Undertone, Vitiligo

August Savage Male Markings (event studs)

Bandit
Cloud, Feline, Mirage, Unders

Outlaw
Cheetah, Feline, Mottled Fissures, Rogue

Ruffian
Feline, Panther, Siamese, Soft Unders

Scoundrel
Feline, Inverted Brawl, Pelage, Undersides

Ukame
Feralis, Marble, Rugged Unders, Undercover

Vagabond
Mirage, Mottled Fissures, Nuzzle, Reverse Indri

exclusive NCL markings (Cinnabar, Clay, Copal, and Marigold)

Any other Tier 3 markings are NOT Breed Only as they can be obtained on any lion through event applicators or Piety in November.


Tier 4 - Rosettes - These markings can show up seemingly at random during breedings! They cannot be selectively applied, but can be passed down from parents with these markings, or spontaneously occur during breedings. They can be randomly obtained with luck from Random Marking Applicators and Total Shuffles.
Even though they can be applied with RMA/Total Shuffle you do not get a choice to have them applied - therefore they ARE Breed Only, due to VERY low chance of getting them from above items. (0.1% chance to get a rosette from RMA/Total Shuffle)

Tier 5 - Hybrid/Restricted Markings - These markings can only be obtained via first generation hybrids (and their offspring) or Gorilla Enclave/Referral Shop marking applicators. They are blocked from being obtained via Random Marking Applicators and Total Shuffles. Only the hybrid markings are considered Breed Only, as the gorilla enclave apps are easy to get if you play daily, for hybrid markings you HAVE to breed to a hybrid/lion with the marking.

Tier 6 - RMA-Exclusive Markings - These markings can only be obtained via Random Marking Applicators and Total Shuffles, or passed down from a parent with these markings. Despite that they are NOT considered breed only as they do have a higher chance to pop up from RMA. (5% chance of RMA exclusive marking when using RMA or Total Shuffle)

RMA exclusive markings (click to go see colors):
Dinictis, Fawn, Feralis, Ghost Feralis, Inverted Quagga, Inverted Zebra*, Maofelis, Mottled Vents, Nimravus, Okapi, Quagga, Zebra

*Most Inverted Zebra colors are raffle only - please make sure to check the Tier listed on the lion page to be able to determine if it's the raffle or rma marking. Raffle markings have (Tier 2) next to them. RMA only colors of Inverted Zebra are: Cimmerian, Noctis. Other Inverted Zebra colors are raffle only.

Skins

Breed Only skins are:
Bunting, Clouded, Echo, Eggshell Blue, Greige, Ink, Lilac, Pale, Peach, Plum, Quail, Ruffian, Sandstone, Welsummer


Mane Shapes and Colors

Breed Only mane shapes are:
Pariah, Royal, Savage, Tsavo

Breed Only mane colors are:
Algae, Amber, Anjeer, Ashen, Briar, Cairngorm, Cameo, Citrine, Champagne, Chartreux, Cimmerian, Cinnabar, Clay, Cocoa, Copal, Dinar, Ebony, Elysian, Fiery, Flaxen, Flint, Fulvous, Goldenrod, Honey, Lilac, Madagascar, Marigold, Nacarat, Orchid, Pearl, Pistachio, Platinum, Prune, Quahir, Sepia, Serruria, Shedua, Slate, Soul, Taupe, Umber

Breed only eyes:

NCL exclusive:
Albinoid, Celadon, Ceramic, Chamotte, Cordovan, Glass, Glaze, Mosaic, Smalti, Terracotta, Tessera

Event Breed only eyes:

February NCL eyes
Dove, Gem, Maroon, Pearl, Rose

April NCL eyes
Daisy, Gazania, Hyacinth, Iris, Flax

May Groupies eyes
Apricot, Banana, Grape

July Raffle lioness eyes
Dawn, Draconid, Galaxy, Neutron, Preon, Starshine, Stellar, Sunglow
Note: Sunglow is also a default eye color for 1st gen tigons

August Studs eyes
Maneater

Breed Unique eyes
Breed Unique eyes are a system where an eye color can "fail" into a unique color, only available from the primary "parent" color - more about them here
Burnish - "fail" from Glaze
Clay - "fail" from Chamotte and Terracotta, one of parents needs to have either of those eye colors
Dunt - "fail" from Tessera
Faience - "fail" from Ceramic
Mire - "fail" from Terracotta
Rose Ebony - "fail" from Smalti
Rose Quartz - "fail" from Cordovan and Glaze, one of parents needs to have either of those eye colors

Combo eyes
Cosmic = Galaxy/Jasper x Dawn, Draconid, Starshine, Stellar, or Sunglow

Breed Only eyes with more than one way of getting
Those are eyes you can sometimes get by breeding two parents who have the eyes that are part of the set (hetero and sectoral) or by getting a May groupie with them. For hetero eyes first color listed is for the right eye, second for left.

Hetero eyes:
Blue & Ice, Cucumber & Saffron, Denim & Jade, Earth & Intense Gold, Ice & Blue, Intense Gold & Earth, Intense Salt & Malachite, Jade & Denim, Malachite & Intense Salt, Saffron & Cucumber

Sectoral:
Amber & Ice, Brown & Blue, Crystal & Lavender, Green & Blue, Pink & Violet, Red & Jet, Sapphire & Albinoid, Tyrian & Indigo, Yellow & Green



And that is all of the actual Breed Only traits. The entirety of this guide is based on official Lioden wiki.