Shaking hands with the other gender is not Islamic protocol or etiquette. It is not a halal (permissible) style of greeting. We cannot say it is haram (impermissible) because the hadith (sayings and traditions of the Prophet) narrated for prohibition are weak. It is not halal (permissible) either. It is makrooh (disliked). Makrooh means that it is better for a Muslim not to perform it. A Muslim of any gender should not perform it unless the situation prefers doing it.