Shray believes that women are incompetent at work and makes statements to this effect, but also makes statements that indicate women must be protected. He is exhibiting:

ambivalent sexism

Explanation:

Ambivalent sexism is a theory that says that sexism is made up of two parts which are the hostile sexism and the benevolent sexism. The hostile sexism has to do with making negative evaluations about a particular gender while bevolent sexism simply means saying something positive about that same gender.

Shray believes that women are incompetent at work and makes statements to this effect, but also makes statements that indicate women must be protected. He is exhibiting ambivalent sexism.