You don’t have to be immunocompromised to get an illness from any animal.
For one example salmonella can be contracted from reptiles. Good hygiene and hand washing should protect anyone.
But bare in mind, more diseases and parasites can be caught from non exotic pets too, for just one example cats:
- Campylobacteriosis.
- Cat scratch disease.
- Cat tapeworm.
- Cryptosporidiosis.
- Giardiasis.
- Hookworm.
- Methicillin-resistant staphylococcus (MRSA)
- Rabies.
I would add Covid too although rare.
Wash your hands, worm your mammalian pets and don’t let your mammalian pets french kiss you 
.
I would never let my dog lick my mouth. No sharing of body fluids 
Edit: worry about mammal pets passing things on more than reptiles. I do.