If your coworkers ask about your living situation, and you live with your parents (being 25-30) would you be embarrassed? ?

No I would ask them why they feel they can ask personal questions like that

You can always tell them you don't feel comfortable sharing that with them. They shouldn't be asking you about that any ways. 

Many people do live with their parents at that age, but some of them help their parents out with things like groceries or running errands. My husband's co worker has his kids living at home and their over 30. I didn't leave the house until I met my husband when I was in my late 20's.

Why would you even answer them? It's not something that they need to know. 

What business is this of theirs?

What matters is whether you feel that your own living situation is appropriate.