The idea of avoiding them in the summer is that you can get fleas from them. After the weather turns colder, the fleas freeze off and you won't have the problem. So the risk from the rabbit itself isn't unreasonably high, just that the rabbit is more likely to have the parasites in the summer.
As an anecdote, the show MeatEater had the host Steve Rinella shoot a jackrabbit while hunting Sage Grouse in Wyoming. The rabbit ended up having fleas due to the weather still being warm. [Unfortunately, I am not able to link to the episode]
Here are some tips for checking to see if your rabbit is infected.
The easiest way to determine if a rabbit or the fleas on a rabbit are a vector for Tularemia is to examine the animal’s liver. If the liver is dotted with white spots, discard the rabbit and wash thoroughly with strong soap.