The Vultures are IN

Fae, Veilspun, Everlux, Spirals: Very poor ability to carry anyone on their backs, rarely even carry their hatchlings this way, preferring instead to use their arms. Instinctual distress from having uninvited weight on their backs. None of their wings are suited to long-distance travel (though Spirals of Wind appear unbothered by it) so these dragons will almost always find alternative means of transportation over long distances that sometimes involve seeking passage on the back of a larger breed. If someone says there was "a dragon perched on their shoulder" the default assumption is one of these four, regardless if the speaker is Dragon or Beastfolk.

Tundra, Gaoler: Biologically wired to be VERY adverse to having any living thing on their backs, but the instinct can be overcome when the creature is expected. They are the Icewarden's perfect custodians by design; they can't be at ease when there's something they can't see grabbing hold of a place they can't strike.

Mirrors: Also biologically wired to be adverse to riders, the instinct is not nearly as strong in Mirrors as it is in Icewarden's children. It is not unheard of for Mirrors who fight alongside significantly smaller dragons to invite the other to act as a mounted lancer, providing not only an adrenaline rush from being a living thing clinging to their neck, but also tactical coverage of weak spots. Mass migration is a natural part of Mirror behavior, so Mirrors have an in-built drive to travel on their own legs and wings instead of someone else's. Guardians: In-built instinct to protect their charge leads to no natural "default" instinct, instead being one that's self-taught once The Search is over. Guardians with charges that won't or can't benefit from being ferried places (or may only be ferried in the Guardian's arms) will usually develop the instinct that living thing on back = threat, cementing that instinct by running scenarios through their head. On the other claw, Guardians with smaller, living charges often develop the mindset that their charge is safest on their back, where they may be carried high in the air away from the threats on the ground. Culturaly, many Guardians will force themselves to overcome their instincts to fully experience the joys of "being big enough to give rides." If those smaller than you feel safe, you are doing much more for the world than protecting only one thing. So long as that other thing is also safe. Snappers: Do not even register something on their back if it's too light tbh. Being largely known as peaceful nomads and having the toughest skin of any Dragon means there's few reasons to fear someone crawling up there for malicious reasons instead of a nap-on-the-go. However, no self-respecting Snapper will let someone do so without asking first, and whether it's on the table at all is decided by either an individual's preferences or Troupe's customs. Regardless of either of these things, it is nearly impossible to stop Snapper younglings from deciding that someone will be giving them a ride. This behaviour has to be taught out before the child encounters a... less-sturdy breed of dragon. Despite younglings seeing no reason that a Snapper cannot hitch a ride on someone else, grown Snappers are not so foolish as to believe that most other drakes can healthily carry their density.

Bogsneaks, Skydancers: Flight-or-freeze reflex is strong in these breeds, neither having the skeletal structure to accommodate riders larger than the smallest breeds of dragon. If something is already on your back, you are hugely disadvantaged and are probably not winning this fight anyway, so either play dead of gtfo. However, both breeds lose this instinct for a brief period of time when a clutch is hatched, being not adverse to carrying their children on their backs until they are old enough to hunt. These two breeds differ in how long they tolerate their children on their backs (or at all), and in how quick they are to accept a ride from someone larger than them. Skydancers have wings for soaring, while Bogsneak wings are... kinda useless. Despite their anti-social trappings, any Bogsneak with more sense than pride will accept a ride when they need to traverse great distances. Tiny Bogsneaks are allegedly fantastic passengers. Dusthides, Sandsurges: Carry others is a completely alien concept to those who have spent the last many centuries underground. No instinct, no culture for it, like putting little snow booties on a cat. Neither of these breeds are suited to long-distance travel, though neither are properly equipped to be a safe passenger on a larger breed due to inherent pointyness in critical locations. That, and Sandsurge aren't exactly small.

Auraboa, Undertide: Again, no cultural concept of ferrying others around. Undertide have a deepsea-typical aversion to being grappled, but Auraboa have no natural instincts around the subject. Regardless, it is nearly impossible for anyone to hitch a ride on these giant snakes even if they wanted to carry someone. Auraboas and Undertides are both so conventionally mobile in the air that there is no culture at all around assisted long-distance travel. Disabled Auraboa and Undertide are often left with whatever courage they can muster to seek help from mixed clans more versed in this kind of cooperation.

Ridgebacks: Ha. Would you look at that, no one's ever asked for a ride on a Ridgeback's back. Wonder why? Ridgebacks have an instinct to start movin' when something is on their back, complimenting their species battle tactics. The cultural aversion to riding a Ridgeback is as much their own concern for the safety of their friends as it is their friend's sense of self-preservation. Given their size and sharpness, Ridgebacks have no living options for rides and rely entirely on contraptions to take them any distance that they cannot (or don't want to) fly for any reason.

Pearlcatchers, Abberations: Not sturdy enough to give rides to other being for long periods of time. Despite Pearlcatchers being stout and Abberations being hardy, their skeletons simply are not meant to hold loads in that way. Pearlcatchers in general have no issue accepting rides from larger folk (though there can be aversion to taking help from an Imperial depending on how and where they were raised), but Abberations have a societal and size-based pressure to seek out non-living means of transportation over great distances.

Wildclaws, Banescale, Vigils: Absolutely not built to carry others on their backs. Exceptions are sometimes made when smaller companions are the ones requesting a ride, but those are rare. The positioning of their torso relative to their legs ensures any load on them feels much heavier than reality thanks to the physics of leverage working against them. Banescale can and do soar when needed, and Vigils spend more time still than in motion, so there is no culture between them of accepting rides from either living or inanimate transportation. Wildclaws have been exposed to multi-species clans for generations, so while their instincts reward them for travelling on-foot, they have no cultural barriers to jump before accepting assistance in long-distance travel, fighting only whatever views their individual upbringings imposed on them.

Imperials, Obelisks: Much too big to receive help from anyone else, much happier giving rides to others. Imperials are physically ill-suited to the task despite their size, as their bodies are long and serpentine and undulate a lot as they gallop to take off, but once they're soaring it's a fine ride for those who can hang on. Imps in mixed lairs often take up the job of ferrying smaller breeds and landbound Beastfolk long distances for lair migration or diplomacy if they aren't the diplomats themselves. Obelisks on the other hand, are the comfiest and fluffiest ride anyone could ask for, and the cozy security of hitching a ride in an Obelisk mane is a Fae's luxury that a Ridgeback could only dream of.

Aether: Instincts for close contact completely muddied by generations in a spacecraft. Aether are not particularly suited for carrying others, but the default response is simply to investigate and move on, without removing the passenger unless it's a burden. Similarly, they have no such inbuilt aversion to contact on top of anyone, and so dragons of equal or greater size to an Aether can expect to gain a rider at random when spending time in an active situation with one.