God bless the Occupy movement.
I would take it seriously. People don't threaten the lives of others. Just because you might disagree with their politics, does not mean it is OK for us to condone death threats or demean their beliefs. I hope she takes it seriously.
I would say take pretty much any kind of threat seriously at first. If and as you have time after that, evaluate it and then you can determine if it's a real threat and not just a bluff or attempt at extortion or intimidation. So the circumstances, time and place and what is known and unknown, must be considered, but in the first moments or minutes until you have time to make a better evaluation it seems best to take it seriously in case it's a real threat that will be carried through quickly.
How seriously you take it depends on the circumstances of delivery. In person, I get serious about it pretty fast in case they move immediately on me. (This doesn't mean I move on them necessarily, but I'm definitely going to consider options including de-escalation, escape, evasion, and even pre-emptive defensive action as appropriate.) By phone or email, I make a perimeter check and ratchet up alertness, give myself a few minutes to settle down, and then I'll think about what I know about it and make a more considered decision as to validity--after I make sure a rifle is in easy reach....