That is wrong.The Federal Reserve is an agency of the government, created by congress. It is owned by the member banks. Don't carry a gun into any of the 12 regional Federal Reserve banks or their branches.
The Federal Reserve is NOT an agency of the government.
The Federal Reserve Act of 1913 allowed the formation of a private bank.
Congress then established the 12 regional branches (so it didn't seem like a monopoly).
Congress also provides the illusion of oversight and supposedly (but never has) altered the powers of Federal Reserve by statute.
If you cannot see this distinction, read this court case where the court rules that Federal Reserve is a private corporation:
Court Rules Fed is Privately Owned
Why is it that you believe that the Federal Reserve is on US government property?
I cannot find any evidence that the government is leasing land to the private bank.
In the case of private property, it is NOT illegal to carry there.
The only offense could be trespass if you do not leave when asked.
(it is not federal property, or an international port, or a school..)