There's some things to like about what I've read so far; postcapitalist thinking with an emphasis on science sounds great, and we do have new tools for political organisation that might let us try new styles of government. Bold ways of trackling automation of labour and the resulting joblessnes are certainly called for.
At the same time, the Wikipedia article claims that they are devoted to doing something either impossible or in a missing-the-point way: deciding social issues using the scientific method, using the carrying capacity of the earth as the sole metric. First: the carrying capacity of the planet is a fair thing to consider in terms of the ramifications of social policy, but it is not comprehensive enough to advocate specific positions on most social policy. If one really wished to nail down value-laden decisions this way, one would need to spell out many more values and some defaults (e.g. "we permit all actions unless they keep us under carrying capacity" or "we forbid all actions unless they keep us under carrying capacity", plus much more). Second: How do we deal with space? Do we expand into it? The proposed metric is silent to a question crucial to its application. Third: Why would we expect people to accept a simple metric like this?
Basically, unless I misunderstand, it fails in the same way Sam Harris does. It tries to provide a metric or method that eliminates all struggle over values, slaps the label of science on it, and tries to end the necessary, messy, nonconvergent field of philosophy that has been with us for all of human history with sleight-of-hand.
As a movement based on this, rather than just a philosophy, we reject it more strongly because in place of the inability to decide problems honestly (as a philosophy), what actually necessarily will happen is that the leaders of the movement will frame issues in ways that seem to be objective that are in actuality based on other factors. They are necessarily guilty of philosophical fraud, at least if Wikipedia is accurate.
I do intend to have a conversation with some of the Zeitgeisters at some point; hopefully with someone who isn't just a follower; someone who knows and doesn't mind being challenged on the philosophy.