Are there people who should not take chemical appetite suppressants?

Yes. People with high blood pressure should not take chemical appetite suppressants. Also, check with your doctor to make sure the active ingredients don't interact with any medications you are on. There is little evidence that appetite ssupressants help with weight loss.
Yes. People with heart disease, trying to get pregnant or pregnant or underweight or very young or very old and frail or using certain medications that may interfere or very difficult to control high blood pressure. Have a complete assessment with a Bariatrician. Benefits of weight management are bountiful but appetite suppressant should be an aid to a multi-pronged approach.
Diet pills. Before prescribing diet pills a complete history and physical is required to added mental cardiovascular and hormone disorders seizures depression and anxiety substance abuse and personal goals and experiance it should be part of a well planned diet and exercise program to avoid failures.
See below. Only those sensitive to the side effects. Those with high blood pressure should be stabilized first; however they can them take the meds in low doses which will work when used in combo with other drugs.