With this change, no one will now check that such companies are actually complying with the law. Fair employment laws are still in place but there's no longer any way to monitor compliance.
If you work in one branch of a company with many locations, you have no way of knowing if your employer is actually complying with the law. In short, nobody knows except the employer itself.
Trump's action has a disproportionately negative effect on the LGBT community, because LGBT people do not have the explicit nondiscrimination protections under federal law afforded other protected minorities. Only about half of the states have fair employment laws that include LGBT people.
The President said he signed this executive order to "create jobs" but it will not create a single job. In fact, it will reduce the number of people employed in large companies because compliance officers will no longer be needed.
This is one of many actions Trump has taken and will take that weaken protections for ordinary Americans and make life more profitable for the wealthy. From environmental rules to employment standards, he wants to make sure the deck is stacked even higher against average citizens.
Trump campaigned like he was the advocate for the "99 percent," notwithstanding he's part of the "1 percent." His actions since becoming President, however, show he's primarily focused on making things even better for those at the top of the heap.
The rest of us are left out in the cold.