Some suttas seem to define "views" as if they are type of stress.
The Avyakata Sutta (AN 7.51), for example, talks about the origin and cessation of views, in the same way that another sutta might talk about the origin and cessation of stress.
The Madhupindika Sutta (MN 18) seems to classify views as papanca and implies they should (like attachments and other obsessions) cease:
If, monk, with regard to the cause whereby the perceptions & categories of objectification assail a person, there is nothing there to relish, welcome, or remain fastened to, then that is the end of the obsessions of passion, the obsessions of resistance, the obsessions of views, the obsessions of uncertainty, the obsessions of conceit, the obsessions of passion for becoming, & the obsessions of ignorance. That is the end of taking up rods & bladed weapons, of arguments, quarrels, disputes, accusations, divisive tale-bearing, & false speech. That is where these evil, unskillful things cease without remainder.
This situation occurs: that when there is the manifestation of reasoning, one will recognise the manifestation of the assault of a number of obsessions and perceptions.
The Kaccayanagotta Sutta (SN 12.15) describes right view:
"By & large, Kaccayana, this world is supported by (takes as its object) a polarity, that of existence & non-existence. But when one sees the origination of the world as it actually is with right discernment, 'non-existence' with reference to the world does not occur to one. When one sees the cessation of the world as it actually is with right discernment, 'existence' with reference to the world does not occur to one.
"By & large, Kaccayana, this world is in bondage to attachments, clingings (sustenances), & biases. But one such as this does not get involved with or cling to these attachments, clingings, fixations of awareness, biases, or obsessions; nor is he resolved on 'my self.' He has no uncertainty or doubt that just stress, when arising, is arising; stress, when passing away, is passing away. In this, his knowledge is independent of others. It's to this extent, Kaccayana, that there is right view.
"'Everything exists': That is one extreme. 'Everything doesn't exist': That is a second extreme.
The "polarity" of existence versus non-existence takes several forms -- all the undeclared questions moe-or-less belong to that category: Does the Tathagata exist after death? Is the cosmos eternal, is it infinite? Are body and soul the same?
So far as I know perhaps the only "right view" is defined by the four noble truths, concerning the origin and cessation of stress, consequently every other view is wrong view. You might argue that anicca and anatta are right views too, but maybe anicca and anatta are better seen as further examples of wrong view, i.e. the view that things are permanent is "wrong", and views about self are also "wrong".
Having a thicket of views isn't the same thing as cessation of stress; and when you're supposed to be concentrating on some other activity, holding views like "I exist" or "I don't exist" are examples of attending inappropriately.
The sutta you quoted (MN 2) is about "fermentations" or asavas. See also the answers to "What is effluent?" -- I think that views in general are categorized as a type (one of four types) of asava.
I think the topic is related to the Vajira Sutta (SN 5.10):
Translator's note: This discourse dramatizes a problem that often arises in meditation practice — a speculative question arises that, if followed, pulls one out of concentration.
What? Do you assume a 'living being,' Mara?
Do you take a position?
This is purely a pile of fabrications.
For only stress is what comes to be;
stress, what remains & falls away.
Nothing but stress comes to be.
Nothing ceases but stress.
If "nothing arises but stress" then views (including the speculative views about existence and non-existence which arise from attending inappropriately) are stress and thus "wrong".
Why is this not a contradiction to anatta?
Bhikkhu Bodhi wrote a footnote to say that this second of six view (i.e. "I have no self") represents a annihilationist/materialist view and is not "anatta".
He doesn't justify/reference that statement/footnote, but having written the answer above I think it's justifiable: i.e. the six views represent eternalism, nihilism, and various other views in between these two extremes.
This answer implies that the doctrine of anatta means "not having a view of self" (it does not mean, "holding a view about non-existence of self") -- and I think that's precisely what's said in MN 22 which is quoted at the top of this answer to What is the precise meaning of anatta?
Perhaps, I don't know, Ven. Bodhi's noting that "I don't exist" is a "materialist" view was also supported or informed by the Visuddhimagga, as it was quoted in Ven. Yuttadhammo's answer.