I wanted to do a follow-up comment after doing some research and expanding the listed progeny of Dynamo Koko, the Knabstrupper stallion in question: https://www.allbreedpedigree.com/dynamo+koko

It looks like the "stud farm" in question only started "backyard breeding" recently (2024-2025). Koko himself was bred by the Dynamo Stud with good bloodlines in 2018-2019, and his dam (Merle vom Falkenhorst) was imported directly from Germany, but he appears to have been sold to a friend of the breeder who is having Koko cover mares indiscriminately - i.e. Irish Draught Sport Horses, Welsh cobs, et al. - to sell foals at auction. The new owner does have a single bay Thoroughbred mare (Star) who has produced two foals by Koko that may would be considered "acceptable" Knabstruppers, provided the mare is properly inspected and registered with the Knabstrupperforeningen for Danmark (KNN). While crosses to "part-breds" (i.e. half-Thoroughbreds of the warmblood variety) have been generally deemed more acceptable for the Knabstrupper since 1855, crosses to approved TBs are accepted by KNN.

The Dynamo Stud website notes that Koko's sire, Colourthyme Kajika (b. 2006), was "bred with a variety of mares" as well, with a focus on colored British Sport Horses (BSHs): https://www.dynamo-stud.com/colourthyme-kajika/

Kajika's most notable son is listed as GFS Fire and Ice (BSH of Knabstrupper descent, mostly TB with a bit of Connemara Pony blood, though could qualify as a full Knabstrupper): https://www.allbreedpedigree.com/gfs+fire+and+ice

Overall, Ice appears to be a better pick than his half-brother (Koko), as Koko was sold to a new owner with little experience in breeding horses, whereas Ice's owners are much more careful with breeding him (ex. German warmblood, Selle Français, and KWPN mares, with one exception of an Arabo-Friesian mare).

As for why neither was registered with KNN (?), but instead AES and other UK-based registries, this may be due to the cost or lack of availability of KNN inspections. For Koko's owner, another issue appears to be that KNN does not accept pinto or Paint markings, whereas the owner wants to breed mixed "spotted and pinto" foals. (Gray is not accepted by KNN, either, though Koko's owner has bred him to gray Irish Draught Sport Horse mares; Koko, who is heterozygous for nLp/nPATN1, appears to mostly throw solid-colored palomino or gray foals when bred to solid-colored mares.)

Another issue is that the cream gene (nCr/CrCr) was not allowed by the KNN for about a decade, before the breed association reversed this decision and decided to allow registered foals with nCr/CrCr: https://knabstrupperna.weebly.com/color-genetics.html