Ice cream by itself is not bad for acid reflux sufferers. There are, however, anatomical and environmental factors that can exacerbate acid reflux. The primary advice is this: If eating a certain food aggravates your acid reflux, then you should avoid that food.
General Anatomy
The lower esophageal sphincter (LES) is a muscular valve at the bottom of the oesophagus. When you swallow, the LES briefly opens to allow food through and then closes until you swallow again. Acid reflux occurs when the LES doesn't close properly, allowing stomach acids back into the oesophagus.
Muscle Tone
Fatty foods, such as ice cream, lower the muscle tone of the LES. Reduced muscle tone makes it difficult for the LES to stay closed when it should, resulting in stomach acid backing up through the LES.
Stress
Ice cream is a comfort food that people eat when they are stressed. Stress causes digestion time to slow. The longer food is in your stomach, the longer active stomach acids are present, and the more likely it is that they will back up into the oesophagus.
Time of Day
Ice cream is a typical evening dessert or snack. Eating and then immediately lying down promotes the situation where stomach acid flows back into the oesophagus.
Gastrointestinal Gas
Lactose, one of the ingredients in ice cream, can cause gastrointestinal gas. Gas can make you burp, and burping can trigger reflux.