No. All laws and rules still apply, even during a shutdown.
The FCC these days is mainly complaint driven dispelling the myth that "Charlie is listening". However, enforcement is still effective and the rules and laws are still in effect despite a lack of funding to the FCC.
On obscenity, these are rarely, if ever handled by the field enforcement agents. Normally, the complaint regarding obscenity comes from a listener including some who may be recording the station, especially if the station has had a history of questionable content. Some more funded organizations may use an aircheck company that works in many major markets that monitors and records the station's air for sale to others, mainly competitors. A similar process can be used for commercial content by a non-commercial station.
On operating over power or otherwise out of tolerance, the complaint will usually come from a station that is being interfered with or in some cases may come from a "competitor" who just does not like the competition. In a written complaint, they can provide information regarding offending station location (if different), take photos of antenna type (if you are running 3 bays instead of 2, etc. or are at an non-compliant height), make recordings, take field strength readings, etc.
In those cases, the station may receive a letter of inquiry from the FCC in Washington (after the government reopens). You must be truthful in your response. Trust me, the penalty for lying to the FCC in a response is far more severe than a couple of F-bombs on the air.
Also, if the out of tolerance operation is interfering with the FAA or other public safety radio systems, the FCC does have a skeleton crew of field enforcement strategic placed throughout the country for safety of life issues. The FCC does have an emergency hotline that is currently staffed. Some may even say that interference to another station (especially from a pirate) could be a safety of life issue because of EAS.
Do yourself a favor, don't regard the shutdown as a ticket to anarchy in the USA, just don't do it... for the good of your station and for the good of LPFM.
This FAQ item was written in response to the December 2018 Government Shutdown.