SELECT P.post FROM fields_post AS P, fields AS F
WHERE (P.value = 'Medium' AND F.name = 'Size')
AND (P.value = 'Purebred' AND F.name = 'Type')
AND P.field = F.id
SELECT P.post FROM fields_post AS P, fields AS F
WHERE P.field = F.id
AND (
(P.value = 'Medium' AND F.name = 'Size')
OR -- это важно
(P.value = 'Purebred' AND F.name = 'Type')
)