The missionary speaks
A missionary trip "safe"? Really, the answer to your question depends partly on what type of trip you are on. Be aware that you are indeed leaving your home country! Some areas of the DR suffer from more problems than others. Basic hygiene and handwashing(take a bottle of hand sanitizer) are important particularly for those going into poor areas. If you are worried about the "natives" eating you alive- don't- they will always cook you first as was mentioned above. I have noticed that American missionaries and other expats seem to suffer from relatively few health problems while those on short missions trips seem to be more prone to stomach problems and other things. It seems that often enough, they bring the problem with them from the states and share it around while they are here. The short answer- be very careful what you eat, drink, where you brush your teeth, etc., stay out of the sun or use sunscreen, use mosquito repellent if needed, keep hydrated (very important), bring your camera, smile, and have fun. Oh, and do try to be respectful and help people. Missionary trips are inherently more problematic than trips to tourist areas for several reasons. Usually, you will be working in poor areas with substandard conditions, often a significant amount of travel is involved, often you will have a hectic schedule and not stay hydrated leading to a much greater likelihood of stomach problems.
BTW, if you really are on a missions trip, I have to assume that you are a Christian. Just how big is your God anyway? Besides, what is the worst that could happen? Die and go to heaven? Ooooh scary. See Prov. 3:5,6.