My background: after 24 years as a veterinarian in private practice, I spent the last 12 years of my working life as a Veterinary Medical Officer in the USDA/Food Safety and Inspection Service, supervising Food Inspectors in packing houses and food processing plants. If an Inspector on the kill floor saw something in a carcass that did not look right he would call me and I was the guy that made the decision about whether or not that animal was fit for human consumption or had to be condemned. When you see the "USDA Insp’d" circle on a cut of beef or a package of sausage, it was processed under the observation of a guy like me. We were trained to spot contamination on carcasses, unsanitary handling, etc.
Cooking kills bacteria. You could safely eat fecal material if you get it hot enough. Not an appealing thought certainly, but it may be reassuring to know that cooking thoroughly pretty well eliminates your risk of food poisoning or getting a parasite. Cooking thoroughly covers sloppy gutting errors. How hot? 165 degrees F is the minimum for poultry. That's the inside temperature. Red meat temperature recommendations are a bit lower. You can find them on the FSIS website. At our house we use a meat thermometer to ensure that the inside temperature of any meat is 165 degrees.
If the animal is not sick with septicemia, which literally means "bacteria in the bloodstream", then bacteria are only going to be present on the exposed surface of the meat. (If you dress out a deer or beef or hog that acts sick and you see abscesses or pus on the entrails, or nasty fluid in the chest or abdomen, take a pass.). This is why it is ok to eat a rare steak from a healthy animal as long as the steak has not been tenderized. Getting the surface temperature above 145-165 degrees kills the bacteria on the surface. The rare interior of the meat is sterile, so eat hearty. Eating fresh raw meat of any kind is risky, inadvisable. Indians in the movies take a bite of raw liver. I won't. Bacteria can also be eliminated by "curing" the meat with salt, sugar, or nitrites (think country ham) or by drying it out to such a degree that bacteria, which need water to survive, are no longer viable (think jerky). There are specific processing parameters that must be met for making safe cured meats and jerky. You can look them up if that is what interests you.
Mechanical tenderizing, and grinding the meat into hamburger or sausage mixes the exposed surface meat with the interior meat, carrying bacteria to the center of the patty. Those who like their hamburgers and sausages rare are taking a risk. Ground meats and tenderized cuts should be cooked to an interior temperature as recommended by FSIS. We cook them to well done and don't worry about it.
USDA regulations require visible contamination to be removed from the carcass by trimming it away with a sterile knife. Rinsing gut contents or hair off with water alone still leaves bacterial contamination on the surface of the meat. Bacteria attach quickly to a surface and simply do not rinse off with water. If there is widespread contamination in the carcass's chest or abdominal cavity, either from the bullet or from sloppy gutting technique, the pleural membrane (chest) and peritoneum (abdomen) should be peeled off the surface of those body cavities. This is why the "gutless" method of field dressing is appealing. Trimming off edible muscle tissue without opening the chest or abdomen eliminates a major potential source of contamination. Hair is dirty, so do your skinning carefully to avoid getting hair on the meat. The gutless method has its own challenges, exposure to blowing dust, flies, dirty hands, slips, etc. But it avoids a lot of problems by not exposing the viscera. If you attempt to remove the rectum and anus and spill some fecal material in the lower abdomen or pelvic cavity, trim out the contaminated area as best you can, cleaning the knife blade as you go, or simply dispose of that part of the carcass after saving the uncontaminated parts.
My previous recommendation to use a mist of vinegar on the meat simply adds another layer of protection against inadvertent bacterial contamination. When I gut a deer by opening the chest and abdomen, I will slosh a quart of vinegar around in the body cavity to offset any sins I may have committed. During this time of year local packing houses are no longer accepting whole deer carcasses for processing, so if my cousin and I get one tomorrow (Missouri's muzzleloader season is still on) we will use the gutless method.
One final thought on temperature: bacteria don't multiply much at all at 45 degrees F or less. So get the meat cooled as quickly as you can. When transporting a deer carcass I usually buy a sack of ice at the first opportunity and place it inside the body cavity to help cool the meat quickly.
This became more of a lecture than I intended. Hope I have answered your question.