First off, we don't have many details about the scenario.
Its apparently a hypothetical but let's say the facts are as they stand, three individuals who are in fact highly allergic to bee stings move in right next store and approach you.
Nowhere in the scenario does it state the neighbors were aggressive, or belligerent or if their approach was passive.
I would think most sane people would have a reasonable discussion about the matter and get the facts.
As a bee keeper and someone who removes and relocates bees for a living, I can tell you that IMO it is virtually impossible for as many people who tell me they are highly allergic to bee stings to be the case.
Any reaction to a bee sting causes some type of response. When someone tells me they are highly allergic I always ask them what their symptoms are and if they have a prescription for an Epi pen (which btw is for two pens).
If after the discussion in our hypothetical, the neighbor is still very concerned but professes she and the two kids are apparently not allergic to the point of anaphylactic shock and feel comfortable enough with me keeping bees next door at least for the time being then, there you go.
You might end the conversation that if at some point they feel uncomfortable again about the bees to please call or knock on your door and we can then take appropriate measures.
If they realize you are a decent person and are concerned about their well being and have been properly educated about bees they may likely leave you alone but I bet in my scenario you will become great neighbors.
If for some reason they come forth again and politely inform you the bees are constantly in their hot tub (as they can see them coming right over your ten foot tall fence to their tub) and (even though they have developed a new appreciation for bees) are just not that into sharing their hot tub with the bees, then of course, the proper thing to do would be to tell them either you will immediately work on a solution or move the bees.
If its not approached like this, they likely will call the police, who will send out animal control, the mayor gets sent a letter, you get a bright orange notice on your door and everyone thinks you are an a-hole, bee keeper and may then stereotype all bee keepers as a-holes.
And let's not forget, you still will have to move your bees.
New bee yards are not impossible to find.