As a millennial ecologist(-in-training), I regularly skim through the TOCs
of most ecological journals, and I certainly see many articles circulated
through email. But a non-trivial amount of my exposure to new science is
through the Twitter feeds of the journals themselves, scientific
organizations, and ecologists I respect. So I'll respectfully disagree
with your implied conclusion that for science to be "taken seriously", we
must remain aloof of social media. Furthermore, if social media is an
avenue for the general public to read about/engage in/comment on science,
then I do indeed think Tweet-ability can be one metric by which articles
are assessed. And perhaps it ought to be, if it encourages researchers to
communicate their science in a way that's accessible to others outside of
their disciplines, to the general public, and even to the Kardashians.