This executive order is a directive to the FTC and FCC, which are both bodies created by congressional law.
As a result, neither has power to violate the first amendment since by virtue of being created by congress, they are subject to the literal reading of “Congress shall make no law”.
For what it’s worth - the 14th amendment passed after the civil war has been read to extend the protections of the bill of rights beyond their literal sense anyway.
By the spirit of the law, no. A lot of historical laws and constitutional writings were to limit power of the government in general. When the constitution was actually written, the executive was just a puppet with military commander powers. But over the centuries there has been power creep into the executive.
Such battles end up in supreme court and the court decides ultimately what interpretation would hold up. The current supreme court is republican/right wing leaning which often ignores the spirit of the law FWIW.
legislative branch - writes the law
judicial branch - interprets the law
executive branch - executes the law
FCC, FTC etc were created by legislative branch to make governing specific areas more streamlined, they are still bound by whatever legislative branch is bound.
I would recommend reading up on historical executive orders held judicial review and how they impacted operations of 3-letter organizations
But if the first words are "Congress shall make no law", does that mean that the President and his executive orders are not bound by the First Amendment?