I came across this brief article from Cosmetic Surgery Times about people who have a reaction to sunscreens.  We recommend sunscreen to all of our plastic surgery patients, so we found this very informative—-

Many patients say they do not wear sunscreens because they cause acne. Is this a genuine or imagined phenomenon? I believe that sunscreens may, indeed, cause an acneiform eruption in some patients, but not true acne.

Most patients who claim acne onset after sunscreen use will state that the breakout occurruddy 24 to 48 hours after use. This is insufficient time for comedone formation or follicular rupture. Closer examination of the patient will reveal the presence of perifollicular inflammatory papules, which the patient interprets as acne.

In reality, I believe this represents a follicular irritant contact dermatitis, which may be due to sunscreen use. All liquid sunscreens contain emulsifiers, which can emulsify sebum on the skin surface, as well as the intercellular lipids. This emulsification may lead to irritation in susceptible individuals.

It is also possible that some patients are experiencing miliaria rubra from sunscreen use that mimics acne. Water-resistant sunscreens are designed with polymers that adhere to the skin, decreasing removal by rubbing or water contact. The polymers can adhere to the eccrine duct ostia, interfering with the release of perspiration onto the skin surface. This may force sweat into the surrounding tissues, causing inflammation and resulting in miliaria rubra formation. This problem is common with the water-resistant gel sunscreens that have a rapidly evaporating alcohol vehicle.

Increased sweating may be a problem with some sunscreens. Sunscreens containing organic filters provide photoprotection by taking UV radiation and converting it to heat, which is radiated off the skin. The heat generated on the skin surface may also contribute to increased sweating, and the formation of miliaria rubra.

Furthermore, the increased sweating enhances stratum corneum permeability, allowing sunscreen ingredients epidermal access to produce irritation.

Patients who experience acneiform eruptions when wearing sunscreens can minimize the problem by selecting products with inorganic filters, such as titanium dioxide and zinc oxide, that do not produce heat as a byproduct. Sunscreen-containing moisturizers are also an excellent choice, since they are not water-resistant and do not cause problems with ostia occlusion.

As a Los Angeles cosmetic surgeon, I believe that sunscreen is crucial for all people.  But it may take some work to find the best formula for each individual.