Certainly most (all?) birds and mammals can get coccidiosis.
However, there are a whole big buncha different species (different genera, in fact) of coccidia. At least seven different species for just chickens!
And different coccidia species
ARE apparently quite species specific. Cattle get cattle-infecting species of coccidia; chickens get chicken-infecting species; cats get cat-infecting species; etcetera. That is not to say that 'crossover' NEVER happens -- for at least some combinations it occasionally does, e.g. humans rarely CAN get poultry coccidiosis -- but it is certainly the exception not the rule, according to present veterinary understanding of the subject.
There are some exceptions like the common Toxoplasma that's easily transmitted from infected cats or dogs to humans, but that's the exception not the rule.
If you do not believe me, a quick perusal of dept of agriculture, vet school and academic information sources, online or in books, should convince you. A sampling of online resources acquired in the first page or so of a quick google:
this
or
this
or
this
(you can find zillions more).
Pat