The short answer: most health authorities say deli meat is fine to eat in pregnancy as long as you heat it until steaming hot first. The concern is Listeria, a bacteria that cold cured or sliced meats can carry. Guidance from the CDC, FDA, ACOG, and NHS informs this page.
Deli meat (also called lunch meat, cold cuts, or sliced meats) includes ham, turkey, salami, bologna, and similar ready-to-eat products, usually eaten cold straight from the fridge. Because these meats are handled after cooking and stored chilled, they can occasionally carry Listeria monocytogenes. The CDC and FDA flag ready-to-eat deli meats as a known source of listeriosis.
Pregnancy makes you far more susceptible to Listeria — the CDC estimates pregnant people are about 10 times more likely to get listeriosis. While infection is rare, it can be serious, and has been linked to miscarriage, stillbirth, premature birth, and infection in the newborn. Listeria is unusual because it can keep growing at fridge temperatures, so simply refrigerating cold cuts does not make them safe. This is why authorities advise caution rather than a green light.
The FDA and CDC advise heating deli meats and cold cuts until they are steaming hot (about 165°F / 74°C) just before eating, which kills Listeria; once heated this way they are considered safe. The NHS similarly advises being careful with cold cured and sliced meats and recommends cooking them thoroughly, and also notes some cured meats may carry a small toxoplasmosis risk. Safe alternatives include freshly cooked meat you heat yourself, canned or shelf-stable meats, and hot meats served steaming.