Using cannabis products, including cannabidiol (CBD), allergic reactions are the exception rather than the rule. In fact, there's no traceable evidence that CBD causes allergies at all. It is not beyond the realm of possibility, however, as people's physiologies differ. Yet it is safe to assume that when taking especially pure CBD, allergic responses are completely unheard of so far. Any symptoms will, more likely than not, be ascribed to other allergens.
Marijuana Allergies or CBD Allergic Reactions?
The only cannabis-related culprit in this regard is marijuana. In fact, preliminary evidence points to CBD having exactly the opposite effect—anti-inflammatory and perhaps even anti-allergenic. Read on for more about this.
First, let's take a look at what could perhaps cause apparent CBD allergic responses after taking a product labeled as cannabidiol. "Apparent," because unfortunately not all manufacturers are ethical, and labels don't always reflect the product content truthfully. Therefore, it's still possible to be duped, meaning the "CBD oil" is perhaps cannabis or marijuana oil.
Cannabis oil and marijuana products are often high in tetrahydrocannabinol (THC), which, researchers are speculating, is probably the allergenic compound in cannabis.
The first case study of a marijuana-associated allergic response was reported as early as 1971, when a young woman had an anaphylactic (very severe allergic) response to smoking weed. 
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While it's not common, it still occurs, and there is even some alarming evidence that allergic responses due to marijuana use are on the rise. This was examined in a recent article published in the European Journal of Allergy and Clinical Immunology (2016):
"IgE‐mediated Cannabis (C. sativa, marihuana) allergy seems to be on the rise. Both active and passive exposure to cannabis allergens may trigger a C. sativa sensitization and/or allergy. The clinical presentation of a C. sativa allergy varies from mild to life‐threatening reactions and often seems to depend on the route of exposure. In addition, sensitization to cannabis allergens can result in various cross‐allergies, mostly for plant foods. This clinical entity, designated as the ‘cannabis‐fruit/vegetable syndrome’, might also imply cross‐reactivity with tobacco, natural latex, and plant‐food‐derived alcoholic beverages." 
In layman’s English, this means the following:
- Marijuana seems to cause allergic reactions in both passive and active smokers.
- The responses vary from mild to very severe, even life-threatening, depending on how it is taken.
- Cannabis sensitization seems to also cause cross-reactivity in allergies, mostly in foods. This means that the proteins in one food source can cause the same reactions by similar proteins in another source. This reaction was so prevalent in fruit and vegetable cross-reactivity with cannabis that it received its own syndrome, predictably called "cannabis‐fruit/vegetable syndrome." The foods most associated with this syndrome are peach, apple, nuts, tomato, and sometimes citrus fruit such as orange and grapefruit. 
Symptoms associated with any cannabis allergy depend on the means of exposure, as said. Smoking or vaporizing, for instance, typically causes respiratory-related symptoms such as rhinitis, conjunctivitis, asthma, and palpebral angioedema. These symptoms, as well as contact urticaria and dermatitis, have also been seen where cannabis was handled directly.
Anaphylactic responses (the life-threatening kind of allergic reactions) have been reported upon ingestion of hemp seed, drinking marijuana tea, and smoking.
The authors of the review also note that the allergic reactions to these plant foods are often triggered or exacerbated by cofactors such as exercise or nonsteroidal anti‐inflammatory drugs (NSAIDs). 
So, if any of these symptoms appear after ingesting, vaping, or applying CBD, the problem may very well lie with the quality of the particular product. Because, as mentioned, so far the evidence points to CBD doing exactly the opposite of allergenic substances.
Is CBD Allergic Reaction a Myth? What Research Says
The rationale is that CBD has been shown, at least in petri-dish and animal studies, to have properties more associated with the treatment of allergic responses than their causation.
For instance, one research article highlighted cannabidiol's anti-inflammatory property in allergic contact dermatitis (ACD), while another demonstrated the efficacy of transdermal CBD as an anti-inflammatory treatment in mice. Inflammation is associated with all allergic responses, and addressing this is always part of the treatment.
Also, allergies are immune responses in the body, as explained in this John Hopkins article on allergies and the immune system:
"When a harmless substance such as dust, mold, or pollen is encountered by a person who is allergic to that substance, the immune system may overreact by producing antibodies that "attack" the allergen." 
These antibodies cause the symptoms associated with any given allergy. The good news is that CBD and other cannabinoids and terpenes seem to mediate this immune response. Continued study is needed, but this compound's potential to not only treat allergies, but also autoimmune and other inflammatory diseases is very apparent at this stage. 
So, based on the available evidence, it is not unrealistic to assume that CBD is not responsible for any allergic reactions. To reiterate, though—not all bodies work the same, and there may be the exception, but there is no clear scientific link between CBD, allergic responses, and allergies. It is also not the experience of millions of CBD users. The compound is used for many purposes and is commonly regarded as safe, even in high doses. Any alarming allergic reaction should immediately be reported to a qualified medical professional.