The US Constitution does not explicitly grant privacy rights, or many other "rights." Individuals have inherent rights which include the right to life, liberty, happiness and the right to keep the fruits of ones labor. Groups on the other hand do not have inherent rights, all rights come through the individual.
The right to life, liberty and happiness would naturally include ones own sexual orientation. So long as one individual does not impose, force or otherwise harm another through their actions then that persons behavior is solely up to them.
The US Supreme Court ruled in Lawrence v. Texas (2003) that "The petitioners [Lawrence and Garner] are entitled to respect for their private lives. The State cannot demean their existence or control their destiny by making their private sexual conduct a crime."
The Bill of Rights and the 14th Amendment contain the areas for which privacy might be expected. States themselves have a large amount of leeway when it comes to privacy expectations in public (10th Amendment). It is generally accepted that no one should expect a right to full privacy in public areas or the Internet.
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Nothing is known of her sexual orientation.
The Joker's sexual orientation is not written into his character.
Soko's sexual orientation is heterosexual/straight.
The fictional character of Yoshi is not depicted with sexual orientation.
Frankie Muniz has not stated his sexual orientation.