Q: Are there workouts that should not be done by people with APT?
Lower abdominal exercises like leg raises, v sit-ups, decline sit-ups, etc., if done incorrectly, can worsen the already tight hip flexors, thus, increasing the APT. Proper positioning of the spine where the back is flat on the floor or the pelvis is posteriorly titled will help improve the APT.
Aside from the exercises, what you need to avoid are daily activities that cause you to assume an incorrect posture like prolonged sitting for several hours, prolonged standing. You need to be conscious of your posture at all times, assuming instead a neutral pelvis, which is the midway between anterior and posterior pelvic tilt. Also, incorporate rest periods by stretching your shortened muscles and by simply walking around just to take the tension off your back.
Strengthening your core muscles is a must in order to avoid APT, and running is one activity that can help strengthen the core muscles as well.