Can neighbor sue you for accidental fire damage caused by your builder?

Anyone can sue any one for most any reason. Being able to collect is a different story.

If you higher a builder you should make sure that they carry Liability insurance and that the property owner is named as an Additional Insured on the builder's policy.

That way, if you are sued for the act of your builder their insurance would protect you and then your insurance, if any, if you are held responsible and will provide protection if the builder does not have sufficient protection.