Michael Sandel has made communitarian arguments for concern with existential risk, along the lines of "the loss of the chain of generations, the dreams of progress, the scientific and artistic and religious and cultural traditions, etc, have value beyond that accruing to individual lives" in his book Public Philosophy.
Derek Parfit briefly considers a similar argument in the concluding section of Reasons and Persons. On this argument, "what matters are what Sidgwick called the ‘ideal goods’—the Sciences, the Arts, and moral progress, or the continued advance towards a wholly just world-wide community. The destruction of mankind would prevent further achievements of these three kinds. This would be extremely bad because what matters most would be the highest achievements of these kinds, and these highest achievements would come in future centuries." (p. 454) However, although not strictly utilitarian, the argument is still broadly consequentialist.
Many people on Less Wrong believe reducing existential risk is one of the most important causes. Most arguments to this effect point out the horrible consequences: everyone now living would die (or face something even worse). The situation becomes even worse if we also consider future generations. Such an argument, as spelt out in Nick Bostrom's latest paper on the topic, for instance, should strike many consequentialists as persuading. But of course, not everyone's a consequentialist, and on other approaches it's far from obvious that existential risk should come out on top. Might it be worth to spend some more time investigating arguments for existential risk reduction that don't presuppose consequentialism? Of course, "non-consequentialism" is a very diverse category, and I'd be surprised if there were a single argument that covered all its members.