You may choose to keep your sexual orientation a purely private matter; nothing requires you to disclose this information to your employer if you do not choose to do so.
However, if you are undergoing discrimination or harassment at work, you may wish to disclose your sexual orientation when speaking with your company's human resources department and/or a member of management to see whether your employer can work with you to solve the problems you are facing. Otherwise, your company may claim it was unaware of your sexual orientation, and as a result incapable of resolving any discrimination or harassment against you on the basis of your sexual orientation.
Also, as more and more people become aware of their gay co-workers, neighbors, family members, friends, and professionals, withholding basic civil rights protections in employment becomes increasingly difficult for an employer to justify, so you may wish to disclose your sexual orientation to your employer for that reason.
If you live in a state or city with provisions which make discrimination on the basis of sexual orientation illegal, the answer would generally be no, especially if other employees are allowed to discuss activities with their spouses or opposite-sex partners, or to display pictures of their spouses, opposite-sex partners, or children on their desks.
In the absence of any legal protections, however, private sector employees are employed "at-will," which means the employer has the right to terminate your employment at any time, for no reason at all or for any reason (including a bad one), so long as the reason is not illegal even if your performance has been outstanding. Therefore, if you disobey your employer's request, you may find yourself without any legal recourse.
If you find yourself in this situation, you may wish to speak with your company's human resources department, other supervisors and co-workers, or a local attorney to determine whether you can work with your employer to resolve this issue. Even if there are not legal protections affecting your employment, you may be able to encourage your employer to voluntarily change its discriminatory policies and/or to educate others in your workplace to help improve your employment situation.
The term "sexual orientation" is generally understood to refer only to whether a person is homosexual (gay), heterosexual (straight), or bisexual, while "gender identity" refers to one's self-identification as a man or a woman, as opposed to one's anatomical sex at birth. Not all transgender people are gay. Many transgendered people identify as straight; many transgender women have male partners and many transgender men have female partners.
While 22 states and the District of Columbia make it illegal to discriminate on the basis of sexual orientation, only nineteen states and D.C. define 'sexual orientation' to either include 'having or being perceived as having a self- image or identity not traditionally associated with one's biological maleness or femaleness, or specifically make it illegal to discriminate on the basis of gender identity. In other states, where courts have analyzed the state's sexual orientation anti-discrimination law, courts have been divided: some narrowly interpreting the laws to exclude gender identity, while others interpret the law to provide some protection with respect to gender identity.
"We know LGBTQ people face higher rates of economic instability, higher poverty, lower rates of employment and higher incidence of pre-existing conditions. You can make a pretty reliable assumption that LGBTQ people are facing serious economic consequences from the pandemic. The idea that LGBTQ people could be more vulnerable simply because of who they are is unacceptable. It was already imperative that we enact these protections, and this crisis has laid bare how critical it is."
–harita Gruberg, director of policy at the Center for American Progress
from The National LGBTQ Advocacy Group Human Rights Campaign and PSB Research