Surprised to see no discussion of this here. Here's a link to the decision: https://www.ca10.uscourts.gov/opinions/13/13-1374.pdf
Basically, a publicly-accessible post office and its parking lot with no security whatsoever is considered "sensitive federal property" therefore the USPS's policy of "no guns 4 u" is permissible.
"Ignoring McDonald‘s command that the Second Amendment does not
protect 'second-class' rights, the Tenth Circuit held that '[t]he risk
inherent in firearms and other weapons distinguishes the Second
Amendment right from other fundamental rights that have been held to be
evaluated under a strict scrutiny test, such as the right to marry and
the right to be free from viewpoint discrimination, which can be
exercised without creating a direct risk to others.'"