закваска which is an ingredient in Bulgarian yogurt is translated as
starter in English. Is this ingredient vegetarian?
Although you mention Google translating
закваска as yeast, I believe it means probiotic cultures instead.
Now, I do not speak or read Bulgarian but I am good with finding patterns and the pattern I found in this word is something that would be translated to speech as 'zakvaska'. If that is how the word is read then I believe it means probiotic cultures.
This does not change much in respect of it being vegetarian, since both yeast and probiotic cultures are vegetarian. Although probiotic cultures are sometimes called live cultures, due to their simplicity and omnipresence, they are not considered as problematic for vegetarians, nor vegans (that is not to say that yogurt is vegan, it is not, but for different reasons).
The essential part of the starter is a bacteria culture (some kind of lactobacillus). Yogurt is always made with a bacterial culture.
Bacteria can be eaten by vegetarians and vegans: they are not animals. They are among the simplest life forms, lacking even a cell nucleus (they are prokaryotes). They are far less complex than plants. Countless numbers of them are harboured and slain by our bodies without any intention on our part.
However, yogurt may sometimes contain gelatin or other non-vegetarian additives.
From what I read regarding yoghurt production, the main (starter) cultures in yogurt are Lactobacillus bulgaricus and Streptococcus thermophilus. The starter cultures are used to convert milk to yogurt during fermentation. As others have mentioned, these are friendly bacteria and not an animal derivative. If you are a strict vegetarian like me, then what we need to look out for mainly is gelatin as Zanna mentioned. Whenever I am not sure what the ingredients are or when the ingredient label is not clear, I always call or email the company to clarify. You may wish to do the same too.