Spray latex paint with an automotive spray gun? Yes, it can be done.
I own every type of spray equipment out there, and have used them all extensively.
With a siphon feed cup gun, (cup on the bottom): Unless you have a professional gun like an old Devilbiss MBC, or Binks model 10, with a large fluid nozzle, you will have to thin the paint excessively. So, you won't usually get a good result. And, you will create a lot of over spray. I don't recommend it.
With a gravity feed gun, (cup on the top): As long as it has a large fluid nozzle, (2.0 or larger), it will be able to spray latex paint. You will still have to thin it.
A HF Chinese gravity feed HVLP will spray latex better than a good siphon feed cup gun.
Automotive spray guns are not ideal here, because they are made to break up the paint, and atomize it into fine particles. You don't do that with latex paint.
So, I would either use a different type of sprayer. Or, a different paint.
An airless sprayer such as the Wagner mentioned, is the better way to go with latex paint. Graco makes nice professional grade, and semiprofessional grade airless cup guns, the latter are reasonably affordable. See Lowe's.
An airless splatters the paint on, using a high pressure pump. I do not have to thin latex, to spray it with my Graco Trucoat.
My exterior doors are all sprayed with automotive paint products. While expensive, with no children to mess it up, it is a finish lasts for the life of the door.
Rustoleum satin finishes are a viable, cheaper alternative.