Beer is the third most popular beverage, behind water and tea. In spite of this, true allergic reactions to beer are rare.

Beer contains four primary ingredients:  Water, malted barley, yeast, and hops.
Barely that has been partially sprouted and then dried is called malt. Malting develops enzymes that break down the starches in the grain to sugars that can be fermented by yeast.  Yeast eats the sugars and produces gas (CO2) and ethanol as waste products.  Hops is added for flavor and as a preservative.  

Nutritionally, beer is mostly water and sugar with a little protein.  A can of regular beer contains about 26 grams of sugar and 1.5 grams of protein. The rest is water.  

For the most part, all allergens (things that cause an allergic reaction) are intact proteins.   Most of the protein in beer is in the form of enzymes that are released from barley in the malting process. After the malting process, when the enzymes have done the work of breaking down complex carbohydrates to be used by the yeast, the mixture is boiled.  Boiling coagulates and precipitates a lot of the protein which is then removed by filtration from the final product. The protein that remains is likely to be in the form of heat resistant enzymes.  

For this reason, the intact protein profile, and hence the allergenicity, of beer is quite different from that of the grains the process started with.   
This may account for the fact beer, the third most widely consumed beverage on the planet, rarely causes true allergic reactions.  As discussed here, allergic-like reactions to alcohol is another story.

Sorting out the cause of a suspected allergic reaction to beer can be a challenge. Allergy skin testing to the most common beer ingredients including barley, malt, hops, and wheat is available and is the place to start. Frequently, a carefully controlled food challenge is required.