There isn't, and states have their own regimes. There's no federal GRC. How federal and state laws interact is beyond my expertise unfortunately.
The nearest to a national standard is the Supreme Court ruling in Bostock v Clayton County, but there are two interesting things about that: firstly, it was a quite narrow ruling in terms of employment discrimination (you can't fire someone merely for being gay or trans-identified).
The other point is that Gorsuch J's reasoning leaned heavily on sex (in its original meaning), so he was taking aim at discrimination on the basis of homosexuality or transgender status that involved employers treating employees differently on the basis of sex. That might mean in terms of dress codes that you can't fire a man for wearing a skirt; if he's wearing fetish gear to work, that might be a different matter.
The judgment is here; the dissent from Alito J is also worth a read.
Executive orders are a thing that come and go with every president. Biden reversed a lot of Trump's EOs on day one, and I'm sure Trump is about to do the same. To bed down any position you need legislation to pass through Congress, or better yet a SC ruling. In terms of Congress, Nancy Mace seems to have the bit between her teeth.