Is it permissible for a Muslim to work as a programmer for a company website that sells forbidden products (alcohol and unslaughtered meat), knowing that he will not add the products himself but will only program the "add product" button?

Your husband's work in programming the commercial website is generally permissible, as long as he does not directly engage in what is forbidden or directly assist in it. Programming an "add product" button does not become forbidden just because the store might add alcohol, pork, or tobacco through it, and no sin attaches to the programmer, as long as the button is not specifically for adding forbidden items, and forbidden items are not the predominant products of the store.