It is that no government can impede your right to free speech...
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press;... etc"
Any business can control the content of any speech of any employee working for them... there is no prohibition against that. (you get into the area of libel laws at that point)
But there IS no "right of free speech" when one is a representative of a free enterprise... hence all that "Duck Dynasty stuff" was just hot air... A&E had every right to do what they wanted... same as this situation.
And RE the 2nd Amendment... "well organized militia..." that seems to be overlooked very often... The way the Swiss handle the gun issue would be perfectly legal under our 2nd Amendment... yet the NRA and their minions would just freak out. Oddly, the Swill model would likely give the US more gun owners... The sad fact is that fewer people own more guns in the US... the current buying frenzy tends to be of people that already own guns... not new owners.