It has been discussed here several times. Yes, according to the law it appears that we could carry into federal buildings, except that there are court cases of people being convicted in court for exactly that. No one here has volunteered to be a test case with the court. If you would like to volunteer talk with your lawyer first.
Here is an article about one such case. The guy ended up being found not guilty because the signs were not posted properly, but nothing regarding 'other lawful purposes.' I believe this has been corrupted to mean 'what we say is ok' or 'except for official purposes.'