Severe allergic reactions to the covid 19 vaccines are very rare (Approximately 1 in 1,000,000 doses) which is why patients are asked beforehand if they have a history of allergies to other vaccines . IgE type 1 immediate type immune reactions mostly occur after a few minutes of injection so the CDC has recommended watching patients for 15-30 minutes after the injection.
If anaphylaxis occurs epinephrine is given and airway management is available.
When patients have a history of allergies to food, bees, dogs, cats, latex this is not a contradiction to having the vaccine. Patients who have a family member who has a history of mild allergy to vaccines but not anaphylaxis is also not a contradiction to a patient not having the vaccine. A history of a severe allergic reaction to a vaccine is however a contraindication to a additional dose of the same vaccine.
It is recommended that the Moderna and Pfizer mRNA COVID 19 vaccines be given alone with at least 14 days before or after a other type of vaccines or allergy immunotherapy including SLIT tablets. The mRNA vaccines are not live vaccines and can be given to immunocompromised patients but these patients may have decreased immune response.
Source: https://www.entnet.org/content/allergic-reactions-related-covid-19-vaccinations-allergic-patients