When amateur radio operators associated with the national weather service "close the net" on a repeater and request only severe weather reports on that frequency, what FCC ruling is in effect, given that this is an amateur radio band?
There is §97.205, which regulates repeater stations:
(e) Ancillary functions of a repeater that are available to users on the input channel are not considered remotely controlled functions of the station. Limiting the use of a repeater to only certain user stations is permissible.
So if the net is on a repeater, the repeater's control operator can decide who can and can not use the repeater, for pretty much any reason. For example, there are some repeaters that are made available only to paying members.
There is also §97.403:
No provision of these rules prevents the use by an amateur station of any means of radiocommunication at its disposal to provide essential communication needs in connection with the immediate safety of human life and immediate protection of property when normal communication systems are not available.
Interpreted somewhat broadly, this can be understood to mean that if the safety of human life is threatened, you can do just about anything you want. Asking people not participating in Skywarn activities to move to a different frequency certainly seems reasonable, and even if there isn't a law requiring it, it's hard to imagine why someone would not comply with such a request.
Also, Skywarn nets are directed nets, which have some structure which may not be regulated, but is at least convention. In particular, there is a net control station who coordinates who can talk and in what turn. Skynet isn't the only such net: there are other directed nets with the purpose of passing third-party traffic and other such activities.
Willfully disregarding the net control station would not be good amateur practice, and so would violate §97.101(a):
(a) In all respects not specifically covered by FCC Rules each amateur station must be operated in accordance with good engineering and good amateur practice.
And also in the same section:
(d) No amateur operator shall willfully or maliciously interfere with or cause interference to any radio communication or signal.
Where "interference" is defined in §97.3:
(23) Harmful interference. Interference which endangers the functioning of a radionavigation service or of other safety services or seriously degrades, obstructs or repeatedly interrupts a radiocommunication service operating in accordance with the Radio Regulations.