I acquired a white flowered clone some years ago, nearly lost it in a bad winter when my heater failed, but it is now healthy and offsetting well.
I was intrigued about the different colour spines and flowers of the while flowered form, and so I managed to contact the original discoverer of this species, Martinez-Avalos.
He told me that "En su habitat mammillaria schiedeana subsp. giselae existen algunos individuos albinos pero muchos acutores la incluyen como una forma albiflora, pero es muy comun ver este color en campo. para mi no existe una clasificacion con la forma albiflora. ".
This means (approximately!) "In the habitat of Mammillaria schiedeana ssp. giselae, there are albino plants which many authors include as f. albiflora, but it is very common to see this colour in the field. To me, a classification of f. albiflora doesn't exist"