Colorado is brucellosis free. Other than hogs, the only states that have it in the wild game are in the greater Yellowstone area in elk and bison, not deer.
Anthrax is not a concern, if an animal were infected it would be obvious there was something wrong with it. It is quickly fatal, hours, and animals that die from it have hemorrhage from the nose, mouth and rectum. You are much more likely to be exposed to anthrax by digging in the dirt. It also rarely affects any animals other than cattle and bison.
That list is essentially any disease that animals get that can also infect humans. Several of them are foreign animal diseases that aren't even found in this country. The majority of them are also vector transmitted diseases, transmitted by insects, not by contact with blood.
Lepto can be found in reproductive organs. The most common route of getting lepto is from contaminated water. Would be very rare to contact it by dressing an animal that has the bacteria.
I'm not against gloves, I wear them. I do it to keep clean, not because I worry about catching a disease. Outside of specific areas of the country getting an actual disease from field dressing or cutting up a game animal is extremely rare.