This actually was a thing that was codified into law, in 1972, by a Democratic-controlled congress, the Equal Employment Opportunity Act. The Democrats recognized that the original Executive Order could easily be repealed by a subsequent president's EO, so they spent the next decade pushing iterations of this act in order to make it federal law, which no president can override with an Executive Order-- by definition, an Executive Order applies only to the Executive Branch of the government, and has zero authority over the Legislative or Judicial branch
The anti-discrimination laws that Democrats created, passed, and codified into law are still in place! Trump's executive order is not able to repeal it, which is specifically why the Democrats got to work, after President Johnson's executive order, getting it passed as an actual law.
Trump's executive order is a piece of political theatre. It has no actual impact on the law, it's intended to signal that anyone who wants to break that law has the support of the Executive branch of the US Government.
But again, no big surprise that "Trump and his party try to do something evil, but are stopped because the Democrats did something right" is being spun as a failure on the part of Democrats by the smug white guy on the nazi-owned, nazi-operated social media platform for nazis, where he has a hammer-and-sickle in his display name! Good thing he proudly admits to being ignorant, because he clearly hasn't even reached "schoolhouse rock" levels of proficiency in History and Civics
