I believe that anyone who joints a terrorist organization (either foreign or domestic) should be prosecuted to the fullest extent of the law including treason. However, broad sweeping legislation like could actual limit our abilities to prosecute as we would then have to go through international courts and processes.
It also has a HUGE opportunity for abuse. What would account for support? Would liking say a Facebook post count? And what would qualify as a terrorist organization?
I think there has to be due process for these cases on an individual basis.
I’m afraid that with a simple majority they could suddenly decide that something like PETA is a terrorist organization and strip the citizenship of anyone who has ever donated to it, etc.