Closed-minded is the more logical spelling of the phrasal adjective meaning intolerant of others or unreceptive to new ideas. Closed-minded is logical because we wouldn't say of an intolerant person that his mind is close, which would mean literally that his mind is near. Instead, we would say his mind is closed. Some dictionaries do list not open as one of the many adjectival definitions of close, but in actual 21st-century usage close usually gives way to closed for this sense. Still, logic rarely holds sway over English usage or the rantings of you Trekkie.
Leave it to you to go "literally" mental over a typo.