exxonmobil.siAfter 15 years of fighting shareholder resolutions, ExxonMobil added sexual orientation and gender identity to its nondiscrimination and anti-harassment policies.
Media relations manager Alan Jeffers confirmed the policy in an email to Dallas Voice:

ExxonMobil’s U.S. Equal Employment Opportunity and Harassment in the Workplace policies have been updated to include sexual orientation and gender identity, which is consistent with ExxonMobil’s long-standing practice of listing enumerated protected classes as defined by federal law.
ExxonMobil’s policies prohibit all forms of discrimination in any company workplace, anywhere in the world.  ExxonMobil supports a work environment that values diversity and inclusion, and has numerous inclusive programs and policies that help make ExxonMobil a great place to work.

The link to the policies are available here.