It's best to avoid sushi made with raw or undercooked fish while pregnant. The FDA, CDC, and ACOG advise against it because raw fish can carry Listeria and parasites, which pose a higher risk in pregnancy. Sushi made only with fully cooked fish, or fish that has been commercially frozen before serving, is a lower-risk choice.
Sushi covers a wide range: raw-fish sushi and sashimi (like tuna, salmon, or yellowtail), cooked options (eel, cooked shrimp, imitation crab, tempura rolls), and vegetarian rolls (cucumber, avocado). The pregnancy questions split into two separate issues. One is whether the fish is raw or cooked. The other is how much mercury the fish contains. These matter for different reasons, so it helps to look at each roll on both counts.
The FDA and CDC advise pregnant people to avoid raw and undercooked fish because of the risk of Listeria and parasites; the CDC notes Listeria infection is far more common in pregnancy and can cause miscarriage, stillbirth, or serious newborn illness. The UK's NHS similarly says to be careful with raw or lightly cooked sushi. Separately, ACOG and the FDA advise limiting mercury by avoiding high-mercury fish such as shark, swordfish, king mackerel, and bigeye tuna. Because raw sushi carries an infection risk the FDA and CDC recommend avoiding, we lean cautious rather than calling it safe.
Cooked-fish sushi, vegetarian rolls, and fully cooked seafood are generally considered acceptable by these authorities, and the FDA actively encourages 2-3 servings a week of lower-mercury cooked fish like salmon, cooked shrimp, and canned light tuna. If you want sushi, favor cooked or veggie rolls and lower-mercury fish. Note the NHS says previously-frozen raw fish is lower-risk for parasites but does not remove the Listeria concern, so authorities still advise caution. When unsure about a specific roll, ask how it's prepared.