Conditions that cause mild to severe allergic reactions
Prior to meeting in sessions, discussion with a players caregiver should specifically confirm any and all allergies and their severities, with which a child might suffer from. These allergic triggers should simply be avoided. If there are several food-based allergies, then food should be restricted from the gaming table, as even designating a separate snacking area may provide complications such as cross-contamination, particulates on hands, and clothing, and even odor as a trigger.
If the allergy is based on environmental conditions that are purely within your control, seek to remedy those conditions, or if that is an impossible option, determine a new playing location. While it may not be ideal for the gaming environments dynamic, consider options for remote play, or hybrid remote play using online technologies such as roll20, fantasygrounds, etc. A purely remote play session would allow all children to be located within their home or location of choice, while hybrid sessions allow for a single player to remotely connect into a device and interact with a seated group.
Communicate with the group what these items to be avoided are in advance of play to prevent any potential risks, and determine from the caregiver proper responses to take in case of an unforeseen allergic reaction, up to and including contacting emergency services.