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Obviously, they are a step up from nonimmigrant visa holders and illegal aliens. And, obviously we treat them better than most nations treat visitors.
But, the question is whether they get that treatment as a matter of right, or whether we just choose to extend them certain privileges until such time as those privileges are abused.

This is not my practice area; I would hire a specialist if i had an issue here. But, I'm guessing it is not as black and white as you say. Green card holders can't vote, they can't sit on juries, their status is not perpetual, and i believe some states have additional requirements for firearms purchases (althiugh they generally can buy guns, which surprised me). They can lose their residency status simply by staying abroad too long, or due to other causes, unlike citizens. So, there are differences between citizens and green card holders. I will leave it to the experts to decide if terrorist supporters can have their residency status revoked, but I certainly don't get why anyone would be upset at deporting a terrorist organization supporter.