Cherries are from the Rosaceae family and therefore not considered to be a citrus fruit. Citrus fruits has a few defining characteristics, such as the high acidity content on the pH scale. Cherries are fairly low on the scale and therefore not very acidic at all.
Some examples of citrus fruits include tangelos, limes, oranges, lemons, rough lemons, and tangelos. Those who have problems with acid reflux will want to avoid eating the above-listed foods as much as possible. If you do in fact have this problem, you will be able to eat cherries because they do not have a high acidic content and therefore will not aggravate the condition.