Martial law means two things in reality; first, that civilians can be tried under military law by military tribunals, and, two, military acting in place of local law enforcement. The former situation applies only to war/civil war and the second requires essentially widespread rioting and lawlessness, which we are indeed seeing all across the nation. In a situation like this, the military would be allowed to assist in restoring order.
Credible reports have indicated that third parties (Antifa, etc.) are exploiting the protests to engage in planned civil disobedience. At this time, the conditions for an active insurrection against the government is in place.
Local police in many areas cannot guarantee safety or enforce the law. Many mayors and governors have refused to take effective action. The conditions to order federal troops in to restore order have been met in many localities.
The need for military to supercede local government applies only when there is the “failure or inability of the legitimate government to exercise its functions on account of the military occupation, or the undesirability of allowing it to do so.” (FM 27-10)
Ordinarily, National Guard troops have roughly the same powers as local police. When they are ordered into federal service, it's a whole new ballgame.
The Constitution does not prohibit use of the military in civilian law enforcement. That is federal legislation, passed by Congress, in the wake of Reconstruction where the Army was the police in the South.
Article 1, Section 9 of the US Constitution states, "The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it." Congress must approve of the suspension and that is unlikely in the current political climate.
This act only applies in cases of war or rebellion; not a mere disaster. Per Ex parte Milligan, the Supreme Court ruled that "martial rule can never exist when the courts are open" and restricts martial law to places where "war really prevails." Unless the civil courts are not functioning, you cannot be tried by military tribunal, held to account under the UCMJ, or held indefinitely. That would be full martial law.
The Posse Comitatus Act prohibits the military from engaging in law enforcement duties. This does not apply to state National Guard units on state missions (it does apply if the state guard is federalized). In 1992, during the Los Angeles Riots, the National Guard, Army, and Marine Corps were ordered into the city under the Insurrection Act, which does allow the military to engage in law enforcement. The current law does not include disasters as reason for deploying the military.
The Insurrection Act requires specific circumstances to go into effect. In short, law enforcement must be unable (in this case) to enforce the law which thus denies equal protection of the law, guaranteed by the 14th Amendment, to citizens. One could imagine that because police are sick or have deserted, things get so dire that rampant rioting and looting threaten a city (or the nation). At that point, ordinary “crime” is so out of hand that it qualifies as “domestic violence,” on par with war. While this isn't exactly full "martial law," it can be considered a form of it.
10 USC §253
The President, by using the militia or the armed forces, or both, or by any other means, shall take such measures as he considers necessary to suppress, in a State, any insurrection, domestic violence, unlawful combination, or conspiracy, if it--
(1) so hinders the execution of the laws of that State, and of the United States within the State, that any part or class of its people is deprived of a right, privilege, immunity, or protection named in the Constitution and secured by law, and the constituted authorities of that State are unable, fail, or refuse to protect that right, privilege, or immunity, or to give that protection; or
...In any situation covered by clause (1), the State shall be considered to have denied the equal protection of the laws secured by the Constitution.
10 USC §254
Whenever the President considers it necessary to use the militia or the armed forces under this chapter, he shall, by proclamation, immediately order the insurgents to disperse and retire peaceably to their abodes within a limited time.
NRS 414.060 Powers and duties of Governor.
3. (g)(5) The conduct of the general public and the movement and cessation of movement of pedestrians and vehicular traffic during, before and after exercises or an emergency or disaster.
(6) Public meetings or gatherings.
National guard powers
NRS 412.602 Right-of-way on public street and highway; penalty for interference. The Nevada National Guard in the performance of its military duties has the right-of-way over any persons or vehicles on any public street or highway of this state, except United States mail carriers, fire apparatus and other emergency vehicles. Any person who hinders or delays, or obstructs, the Nevada National Guard in the performance of its military duties is guilty of a misdemeanor.”
No gun regulations/confiscation
42 US Code §5207
(a)Prohibition on confiscation of firearmsNo officer or employee of the United States (including any member of the uniformed services), or person operating pursuant to or under color of Federal law, or receiving Federal funds, or under control of any Federal official, or providing services to such an officer, employee, or other person, while acting in support of relief from a major disaster or emergency, may--
(1) temporarily or permanently seize, or authorize seizure of, any firearm the possession of which is not prohibited under Federal, State, or local law, other than for forfeiture in compliance with Federal law or as evidence in a criminal investigation;
(2) require registration of any firearm for which registration is not required by Federal, State, or local law;
(3) prohibit possession of any firearm, or promulgate any rule, regulation, or order prohibiting possession of any firearm, in any place or by any person where such possession is not otherwise prohibited by Federal, State, or local law; or
(4) prohibit the carrying of firearms by any person otherwise authorized to carry firearms under Federal, State, or local law, solely because such person is operating under the direction, control, or supervision of a Federal agency in support of relief from the major disaster or emergency.
(b)Limitation Nothing in this section shall be construed to prohibit any person in subsection (a) from requiring the temporary surrender of a firearm as a condition for entry into any mode of transportation used for rescue or evacuation during a major disaster or emergency, provided that such temporarily surrendered firearm is returned at the completion of such rescue or evacuation.
(c)Private rights of action
Any individual aggrieved by a violation of this section may seek relief in an action at law, suit in equity, or other proper proceeding for redress against any person who subjects such individual, or causes such individual to be subjected, to the deprivation of any of the rights, privileges, or immunities secured by this section.
NRS 414.155 Limitations on emergency powers relating to firearms. Pursuant to Amendment II of the Constitution of the United States and Section 11 of Article 1 of the Constitution of the State of Nevada, and notwithstanding any other provision of law, the emergency powers conferred upon the Governor and upon the executive heads or governing bodies of the political subdivisions of this State must not be construed to allow:
1. The confiscation of a firearm from a person unless the person is:
(a) In unlawful possession of the firearm; or
(b) Unlawfully carrying the firearm; or
2. The imposition of additional restrictions as to the lawful possession, transfer, sale, carrying, storage, display or use of:
(b) Ammunition; or
(c) Components of firearms or ammunition.