I am not a lawyer but the “government” can sue and be sued in civil actions. For instance, in the late 1990’s, I worked for an attorney who sued the then-POTUS in a civil suit regarding the Panama Canal Treaty. Government officials are sued not as individuals, but in their official capacity. That particular suit went thru the federal district court, the district court of appeals and to the SCOTUS. It was a civil suit.
I think there is a misunderstanding of just what a ‘civil suit’ is. The federal courts (where the Snyder v. Phelps case was held) recognize only civil, criminal, bankruptcy cases. There is no such thing as “government cases” per se. Government agencies are afforded some special considerations in federal court (more time to answer, etc). There are also administrative agencies that handle government cases. That is a separate body of law (other than Article III courts) known as Administrative Law. The parties in federal court cases are irrelevant, so long as they are sued properly (as an individual, a corporate entity, a government official AS a government official not as an individual).
Criminal cases are pursued by goverments, i.e., local municipalities, states, federal government in the appropriate court. If you are a victim of a crime, the government pursues that as a criminal case, i.e., OJ Simpson was pursued in his criminal matter by LA in a municipal court, and in the civil matter was sued by the Goldmans.
According to Blackstone, there is a difference between “private wrong” and “public wrong.” The “private wrong” where a private person or entity or the government acting as or being sued as an entity, can go into court and sue (or be sued). The government, acts on behalf of the state in “public wrong” caes, acting on behalf of all the people.
Can civil suites can be used to restrict or award damages for constitutionally protected freedoms? Can a court give another person the right to restrict my free speech solely because it offends them (not libelous, not slanderous, not meant solely to intimidate or enrage)?