I prefer to avoid all forms of dairy in small animals and most other animals.  Yogurt is cultured enough most can eat it but it still does contain lactose and someone with severe lactose intolerance which includes most animals may not even be able to eat yogurt.  Humans are the only animals that maintain the ability to digest lactose and other sugars in milk through adulthood and even then in some races up to 90% become lactose intolerant by old age.  Both humans and animals can make up for this fact by growing a certain bacteria in the digestive tract that will take the place of the lactase enzyme that breaks down lactose.  However this bacteria has to be fed constantly so if you (or your animals) never get any dairy and are then suddenly given some several days in a row major symptoms can result to the point of bloody diarrhea.  This is a very bad thing to have on top of other illnesses in small animals. 
Yogurt is really pointless.  There are plenty of capsules and powders out there that have all the bacteria needed.  For guinea pigs we just take droppings from a healthy pig, dissolve in water, and syringe to the sick pigs.  They get all the digestive tract bacteria needed that way and guinea pigs common eat cecal pellets.  For other animals just buy acidophilus capsules or any colon health product that doesn't contain other ingredients like fiber.  I've got about 5 different kinds of pills all with different strains of bacteria for digestive tract health.  It's easy to find something without dairy to give them.  ACV with the mother in it will also contain a lot of things that aid in digestion.  Canned plain pumpkin can help prevent loose stools if the bacteria does die off.