There have been a number of enquiries from parents as to whether children with asthma, eczema, hayfever, and/or food/insect allergies can have the mRNA COVID vaccines (Pfizer for children 5 years+; Moderna for children 12 years+). The Australasian Society of Allergy and Immunology have a great question and answer web-link to address concerns parents may have (see this: https://www.allergy.org.au/patients/ascia-covid-19-vaccination-faq).
There is no evidence that people with allergic conditions such as asthma, hay fever (allergic rhinitis), food allergy or insect sting allergy are at any greater risk of an allergic reaction to the mRNA COVID vaccines compared to the general population. No special precautions are required in such individuals, even those who carry an adrenaline auto-injector for their food or insect allergy.