This article specifically addresses Visa applications. So, if the person is already applying for a citizenship, there is most likely already a residency which doesn't require Visa on entry. There also seems to be a different set of rules for people already in the country. From the article:
And while the court recognized the First Amendment rights of noncitizens currently present in the United States who limit their online speech because they may need to renew a visa in the future, it held that the federal government’s regulation of immigration should be granted significant deference.