The Allergy Dude strongly recommends everyone get routine aerobic exercise, provided they do not have a medical condition that prevents this. For example, if you have asthma, this should be under tight and good control before attempting exercise. Thus, when I see new patients or ill followup patients, I may restrict their exercise levels, until tight control is achieved. Then they should slowly and consistently increase the amount of their aerobic exercise.
The types of aerobic exercises that The Allergy Dude recommends include running, rowing, hiking, biking, and swimming. Basically, triathlon type of exercise. The medical literature has examined the issue of whether regular swimming indoors, which involves prolonged exposure to chlorinated water, can increase the rate of allergies and asthma in patients (see PubMed search for example of studies). There is disagreement in the literature. Some studies suggest yes and others suggest no. The latest study The Allergy Dude is aware of is reassuring. Laia Font-Ribera and associates examined this issue in their article "Swimming Pool Attendance, Asthma, Allergies, and Lung Function in the Avon Longitudinal Study of Parents and Children Cohort", which was published in the American Journal of Respiratory and Critical Care Medicine Vol 183. pp. 582-588, (2011). "Swimming did not increase the risk of asthma or allergic symptoms in British children. Swimming was associated with increased lung function and lower risk of asthma symptoms, especially among children with preexisting respiratory conditions." The Allergy Dude's opinion is that the benefits from swimming far outweigh the minimal risks.