It’s very common for people to be allergic to latex and if they are then you shouldn’t be surprised if they are also allergic to acrylic. A common solution would be to get them into hard gel because you could perform enhancements and customize their nails using gel instead of acrylic. What do you do when they have a reaction to both acrylic and gel? An individual with extremely sensitive skin can they get their nails done?
One idea is to use a primer and dehydrator. Try young nails protein bond might be a solution. The reason is because it’s made as the same keratin protein as human nails. So that shouldn’t cause a reaction.
Next even if you have tried hard gel. There is Polygel which might work if you use a bonder instead of a primer. If they have a reaction to the polygel think about what other products was used when you did the service it most likely isn’t being caused by the polygel but something else that is coming in contact with their skin during the service.
Make sure if you are using gel that it is cured properly. You might need to use a different UV light.
The problem is most likely a adhesive allergy and it will only get worse if you keep trying with products that have an adhesive. Most good nail salon used products that include some kind of adhesive.