The issues arrived in separate cases, but they boiled down to the same question: Does the Civil Rights Act of 1964, whose Title VII outlaws workplace discrimination based on sex, nevertheless permit employers to fire individuals because they are gay or transgender?

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Under Supreme Court precedent, employers can’t discriminate against workers who don’t conform to follow sex stereotypes, for instance, effeminate men or aggressive women. Pamela Karlan, a Stanford law professor representing the gay men, said it followed that firing a male employee who is attracted to men while taking no action against a woman who dates men was equally impermissible. “That’s discrimination because of sex,” Ms. Karlan said.