What have I missed about the immune system interacting with mosquitoes? The primary immune response I'm aware of that an organism would have with its food would be a food allergy. Are you worried that the genes would jump from a human-biting mosquito species to a bird-biting species and the males would somehow mutate to also bite? Mosquitoes don't infect the animals they bite, so I don't think our allergic immune responses to their bites are beneficial in any way.
Also, ever since a wilderness survival course in a Wisconsin forest in the mid 1990s exposed me to tons of mosquito bites, my immune response to female mosquito saliva is very suppressed to non-existent. (I no longer swell up or feel itchy when bitten. I presume I still have some immune response that could be measured by some blood test, but it's nothing I can notice, even if I look closely at a spot where I've seen a mosquito bite me.) Is there something I need to worry about my reduced immune response to mosquitoes?
Note that only female mosquitoes bite - blood is a necessary component for their eggs to form.
Personally, I’d most question the potential effect on the food chain—what if birds, for example, started developing allergies or other autoimmune issues because of this or other new/modified proteins in resulting male mosquitoes that their immune systems don’t recognize?