If this happens, the people who are caring for you are prepared for it. They will immediately remove it and clean you up. They will not say anything about it.
Some women let this fear interfere with their pushing efforts. This is not necessary. While you may be worried, those around you are used to the occurrence.
Some women will have loose, frequent stools leading up to labor. This can act like a natural enema. Some women choose to do an enema at home in early labor to try to clean out their colon. This can be miserable and potentially lead to dehydration. Though this will not necessarily prevent the presence of stool during your labor or birth.