There have been numerous legal attempts to argue laws against sexual discrimination must include sexual orientation. Some have been successful and some have not.
The current position of the EEOC is sexual orientation is included in laws that prohibit sexual discrimination in employment practices. While that isn't the same law that protects sexual discrimination in housing practices, it's not that much of a leap in jurisprudence.
Overview
EEOC interprets and enforces Title VII's prohibition of sex discrimination as forbidding any employment discrimination based on gender identity or sexual orientation. These protections apply regardless of any contrary state or local laws.
Through investigation, conciliation, and litigation of charges by individuals against private sector employers, as well as hearings and appeals for federal sector workers, the Commission has taken the position that existing sex discrimination provisions in Title VII protect lesbian, gay, bisexual, and transgender (LGBT) applicants and employees against employment bias. The Commission has obtained approximately $6.4 million in monetary relief for individuals, as well as numerous employer policy changes, in voluntary resolutions of LGBT discrimination charges under Title VII since data collection began in 2013. A growing number of court decisions have endorsed the Commission's interpretation of Title VII.
https://www.eeoc.gov/eeoc/newsroom/wysk/enforcement_protections_lgbt_workers.cfm
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