Hiya, 
Well, you said most of this before in different words, but I still think you’re reading the sutta incorrectly. Let me explain in more detail, then.
The pronoun “they” refers to the unlearned ordinary person who has not seen the noble ones, etc. throughout the entire sutta. In Pali there isn’t even a pronoun at all, and the repeated verb “regard” (samanupassati) refers back to the unlearned ordinary person (assutavā puthujjano) the entire time. This is hard to explain if you don’t know Pali, but if you do, have a look. The na eva construction also indicates that these statements form a continuum and there’s no separation between Buddhist and non-Buddhists. Again, Pali students will understand what I’m saying.
It also becomes clear when we expand the elipses (the triple dot, where stuff has been omitted for sake of brevity):
Perhaps they [i.e. the unlearned ordinary person] don’t regard form or feeling or perception or choices or consciousness as self. Still, they have such a view: ‘The self and the cosmos are one and the same. After passing away I will be permanent, everlasting, eternal, and imperishable.’ But that eternalist view is just a conditioned phenomenon. And what’s the source of that conditioned phenomenon? When the UNLEARNED ORDINARY PERSON is struck by feelings born of contact with ignorance, craving arises. That conditioned phenomenon is born from that.
We can do the same for the annihilationist view, but you get the point.
Now, this unlearned person could be a Buddhist or not. Whatever religion they follow is not important. The point is that they views are all equally wrong views, and both Buddhists and non-Buddhists can have wrong views. There’s no distinctly Buddhist-only views here.
Since you yourself do not regard the five aggregates as self, in your view the ”I” or self can only cease to be thanks to something else than the five aggregates….
Nibbāna?
I would appreciate it if you don’t try to tell me what my view is, because it’s not this. 
You seem to misunderstand something here. I don’t think there is a real “I” or self at all, so it can’t cease either.
You’re addressing the view of the annihilationists instead. And you seem to assume there are just the five aggregates and nibbāna, nothing else. Fair enough. But that is not the assumption of the eternalists and annihilationists make in this sutta. Not necessarily being Buddhists, they probably don’t even believe in nibbāna in the first place. But more importantly, some of them think there is still a self or “I” outside of the aggregates—that’s the point I perceive is being made here. That self or “I” could for example be the incorrectly perceived owner or experiencer of the aggregates. Eternalists think this continues forever after death; annihilationists think it is destroyed at death. But since such a thing doesn’t exist in the first place, both views are wrong.
It’s never said what “it” here refers to, actually. Since it’s in the singular and the aggregates are always referred to in the plural, it likely doesn’t refer to the five aggregates specifically. Although they are in some sense included, of course, the “it” seems to me to refer to “the all” or existence in general. Not all suttas are analytically separating everything into the five aggregates.