The Equal Employment Opportunity Commission (EEOC) is important because it is the primary federal agency charged with eliminating prohibited discrimination in the workplace in the United States.
Title VII of the Civil Rights Act prohibits discrimination "on the basis of sex," and that law is specifically assigned to EEOC for enforcement. Over the past decade, EEOC has gone on record with the position that discrimination on the basis of sexual orientation and gender identity fall within the scope of discrimination "on the basis of sex." EEOC has therefore accepted and processed complaints of discrimination on behalf of employees facing discrimination at work for being gay or trans. Most federal courts ruling on these cases have deferred to and followed the determination of EEOC, because it is the lead agency of the government in opposing workplace discrimination and is considered to be "expert" in the field.
Right-wing politicians like Senator Lee are busily engaged in the effort to roll back the definition of "sex discrimination" to a standard that covers discrimination ONLY on the basis of biological or genetic sex. This, of course, would strip gay and trans folks of their right to be free of discrimination in the workplace.
In short, Senator Lee would like to force us all back into the closet at work.
Chai Feldblum has been one of the EEOC Commissioners who are protective of gay and trans rights at work. She is also an "out" lesbian, so there is also a nasty overlay of personal bigotry involved in Senator Lee's action to block Feldblum's reappointment to the Commission.
Take this seriously, folks! Right-wing politicians are attempting to do away with your rights. They fall back on "religious" arguments to do so, as if YOUR gender identity somehow deprives THEM of their rights to religious belief. It's a totally phony argument. But it's exactly what they're doing.