To what extent is it religiously permissible to work for an Egyptian-Israeli company that operates in the clothing industry?

As long as the company's field of work is clothing manufacturing, the basic ruling is that it is permissible to work there. The fact that it is an Egyptian-Israeli company does not affect its permissibility, unless its existence and working for it lead to prohibitions or harms that affect Muslims, in which case it becomes forbidden to work for or deal with it.