This will not work, to briefly explain why I think so:

For the intended audience of the article, Libertarianism is unusual, Liberalism is normative. If the community was completely liberal, its liberalism would not have more than one mention or so in the article, certainly it would not make the title.

The prevalence of Liberals and Socialists, no matter how emphasized, can not lead to a rebranding as long as there is a presence of Libertarians in a fraction greater than expected. Indeed even if Libertarians were precisely at the expected fraction, whatever that would be, they might still get picked up by people searching for weird, potentially bad things about this weird, potentially bad "rationality movement".

As evidence of this note no journalist so far considers the eeire near total absence of normal conservatives who make up half of the population of the United States, the country most strongly represented, to be an unusual feature of the community. And furthermore if they somehow made up half of the community or some other "representative" fraction, this would be seen as a very strange, unusual perhaps even worrying feature of the community.

Hypothetically the opposite effect should be seen as well, if somehow this place was 100% liberal, yet still in the weird, potentially bad mental bin of journalists, its weirdness and badness would lead to its liberalism not being mentioned. For an example of this consider if you associate the Jim Jones' Family, the mass suicide of which gave rise to the phrase "drinking the cool aid", with liberalism or socialism.

The only way to inoculate would be to loudly denounce and perhaps even purge libertarians. Perhaps a few self-eviscerating heartfelt admissions of "how rationality cured my libertarianism" for good measure. This wouldn't actually result in no Libertarians being present of course, though it would dent their numbers, but it would provide a giant sign of "it doesn't make sense to use this fact about the community". This doesn't always work, since denouncing the prominence of witches or making official statements about how they are unwelcome has been read as evidence for the presence of witchcraft by journalists in the past as well.

Beyond the question of if it would work, I would like to more generally disapprove of this approach, since it would rapidly hasten the ongoing politicization of the rationality community, badly harming the art in the process. To make a step beyond that I will also say that I think many libertarian rationalists carry interesting insight, precisely because of their ideology.