In case you weren't paying attention, the main reason for this round of protests is that Trump's executive order is causing legal permanent residents to be detained in US airports and/or deported from the country.
Regardless of whether or not a visa is needed, the border guard has final say on whether or not a foreign citizen is allowed to enter the country.
Citizens have freedom of entry into the country, there is no way they could be barred.
Green card holders are not exempt from the order as per advice from the whitehouse itself. The DHS initially thought they would be exempt, but were later corrected by Trump.
A US citizen is also required to present their US passport when entering the US - even if they are a dual citizen and hold another passport.
The whole thing about dual citizens refers to citizens of the banned countries who also hold citizenship of a third country - i.e. one that is not the US and one that is not banned. e.g. an Iraqi-Canadian who presents a Canadian passport is still barred from the US by Trump's order.
It is impractical for a foreign citizen living overseas without ties to the US to sue the US government for wrongfully denying them entry to the country even though they had a visa. It would be simpler and cheaper for an individual with the means to pull this off to simply apply for an investment-based green card[0] or to get a Maltese passport.[1] Malta is on the list of Visa Waiver Program countries.
[0] https://www.uscis.gov/green-card/green-card-through-job/gree...
[1] https://www.ccmalta.com/publications/malta-citizenship-inves...