I suppose it's possible to hurt yourself with tire glue but I had no issues gluing my tires over 25 years and 70,000 miles except very sticky, hard to clean fingers. (Tubasti - several boxes worth and Clement for my race tires plus another glue or two over the years.) And that's from a guy who sensitized himself to a wide variety of solvents building fiberglass boats. Now, the solvents some use to clean the rims is another story. I don't think I ever did more than scrape off old, hard glue and never saw the need to "clean" the rim, seeing a clean rim as inferior to a rim covered with really stuck old glue. That glue isn't going to care about your dog's hairs; they'll just be part of your ride. You might notice them first stop (in your brake pads). Humidity isn't going to affect the glue. All the high outdoor temperature will do is thin the glue a little and make it messier to work with as well as probably making it harder to stick the tire down properly but easier to move if it is not quite right.
Ben