I'd categorise interaction with Cthulhu on the same level that I'd categorise sticking your hand in a bonfire.
Only:
1) Cthulhu's a creature, and therefore subject to classification by alignment in D&D.
2) It's no accident that Cthulhu's designed specifically to hurt people.
I think point (2) takes away Cthulhu's right to immunity of intention towards evil in the same way, say, the smallpox virus has. Evolution might have designed the smallpox virus as being uncaring and predictably malignant towards humans, whereas an author who does the same sets out specifically to create a monster - the uncaringness is just flavour.
I'll admit that this is inconsistent - isn't a rot grub neutral, and predictably malignant? Yes, but perhaps it falls under the animal clause because it's of animal intelligence, and resembles an animal. Cthulhu, on the other hand, schemes towards his malignant effect, and I think we associate malignancy + intelligence with wickedness.
This is subjective, but then, morality itself is inconsistent. One example I've seen repeated recently is the following scenarios:
1) "You and an obese guy are on a train speeding towards 5 people on the track who cannot get off. You have the option to flick a switch and divert the train to another track where only 1 person is trapped, killing them rather than the 5. Do you flick the switch?"
2) "You and an obese guy are on a train speeding towards 5 people on the track who cannot get off. There is no switch and alternate track this time. You could push the obese guy off the front of the train, which would slow it enough to save the 5 people but kill him. Do you push him off?"
Given that most people don't hesitate to flick the switch in the first instance, but cannot bring themselves to push the obese guy off in the second suggests that morality cannot be approached in terms of logic, only in terms of human idiosyncracy. Mine tells me that Cthulhu is evil because I know what the true story purpose of his creation was, and he resembles a devil more than an animal. The tipping point for me is that he schemes against humanity, and thus cannot fall back on low intelligence as an excuse for his actions.