Unfortunately, not all cultures are allowed on the SCD. Following is a quote from pecanbread.com:
The yogurt you buy can contain Lactobacillus Acidophilus, Streptococcus Thermophilus, and Lactobacillus Bulgaricus. It must not contain Bifidus/Bifidum bacteria. Nor should it contain gums, sugars, or additives, or flavors of any kind.
In reading the ingredients for White Mountain Bulgarian Yogurt, it contains Bifidum. If we can only get White Mountain to exclude it, they'd have an instant customer base with all those who follow the SCD!