Are wooden spoons sanitary?

If they're cared for properly, absolutely.

Wash them [by hand] in warm soapy water after using them and toss them in a drying rack to dry. Good as new.

Avoid letting them soak in water or with dirty dishes for days. Don't put them in a dishwasher.

When they start to dry out, you can reapply some finish. I sell some spoon finish in my shop, or a cutting board oil would work great.