TL;DR

Rebirth view, for someone who still clings to self view, can be used as skillful means (upaya) to remove the habit of misconduct, cultivate virtue and generate the path to liberation. Rebirth view is the middle way and is the right view with effluents/ taints.

Denying rebirth-of-self view while clinging to self view is wrong view, because this is annihilationism and brings the unenlightened to hedonism.

Denying rebirth-of-self view after discarding self view is the noble right view. Rebirth without self view is simply the continuation of suffering and the continuation of the chain of conditioned processes. It's not about the rebirth of a specific person or being or self or consciousness.

Rebirth in Buddhism is not falsehood. It's not truth. It's just skillful means (upaya), a helpful tool. A middle way between falsehood and truth.

Long answer

Denying rebirth-of-self, while clinging to self-view, appears to be wrong view. This is unskillful means because it directs the mind of the unenlightened towards hedonism and nihilism. This is also the view of annihilationism.

And what is wrong view? 'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no contemplatives or brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is wrong view.
MN 117

Holding on to the rebirth-of-self, while clinging to the fetter of self view, is a right view with effluents/ taints.

"And what is the right view with effluents, siding with merit, resulting in acquisitions? 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. There is mother & father. There are spontaneously reborn beings; there are contemplatives & brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is the right view with effluents, siding with merit, resulting in acquisitions.
MN 117

Why is this the case? This is because siding with merit, one could use this as skillful means (upaya), a helpful tool, to remove the habit of misconduct, cultivate virtue and generate the path to liberation.

The Buddha is the doctor (Iti 100) who treats the illness which is suffering (dukkha). This is a medicine that he has prescribed.

“And for the sake of what benefit should a woman or a man, a householder or one gone forth, often reflect thus: ‘I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do’? People engage in misconduct by body, speech, and mind. But when one often reflects upon this theme, such misconduct is either completely abandoned or diminished. It is for the sake of this benefit that a woman or a man, a householder or one gone forth, should often reflect thus: ‘I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do.’ .....

“This noble disciple reflects thus: ‘I am not the only one who is the owner of one’s kamma, the heir of one’s kamma; who has kamma as one’s origin, kamma as one’s relative, kamma as one’s resort; who will be the heir of whatever kamma, good or bad, that one does. All beings that come and go, that pass away and undergo rebirth, are owners of their kamma, heirs of their kamma; all have kamma as their origin, kamma as their relative, kamma as their resort; all will be heirs of whatever kamma, good or bad, that they do.’ As he often reflects on this theme, the path is generated. He pursues this path, develops it, and cultivates it. As he does so, the fetters are entirely abandoned and the underlying tendencies are uprooted.
AN 5.57

Once self-view is discarded, rebirth-of-self view will also be discarded. This is the noble Right View.

"And what is the right view that is noble, without effluents, transcendent, a factor of the path? The discernment, the faculty of discernment, the strength of discernment, analysis of qualities as a factor for awakening, the path factor of right view in one developing the noble path whose mind is noble, whose mind is without effluents, who is fully possessed of the noble path. This is the right view that is noble, without effluents, transcendent, a factor of the path.
MN 117

How do we know that rebirth-of-self view will be discarded? This is the higher teaching for those who have understood anatta, as taught in MN 38 and SN 22.85.

Rebirth without self view is simply the continuation of suffering and the continuation of the chain of conditioned processes. It's not about the rebirth of a specific person or being or self or consciousness.

“Yes, friend,” he replied, and he went to the Blessed One, and after paying homage to him, sat down at one side. The Blessed One then asked him: “Sāti, is it true that the following pernicious view has arisen in you: ‘As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another’?”

“Exactly so, venerable sir. As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another.”

“What is that consciousness, Sāti?”

“Venerable sir, it is that which speaks and feels and experiences here and there the result of good and bad actions.”

“Misguided man, to whom have you ever known me to teach the Dhamma in that way? Misguided man, have I not stated in many ways consciousness to be dependently arisen, since without a condition there is no origination of consciousness? But you, misguided man, have misrepresented us by your wrong grasp and injured yourself and stored up much demerit; for this will lead to your harm and suffering for a long time.”
MN 38

“But, friend, when the Tathagata is not apprehended by you as real and actual here in this very life, is it fitting for you to declare: ‘As I understand the Dhamma taught by the Blessed One, a bhikkhu whose taints are destroyed is annihilated and perishes with the breakup of the body and does not exist after death’?”

“Formerly, friend Sāriputta, when I was ignorant, I did hold that pernicious view, but now that I have heard this Dhamma teaching of the Venerable Sāriputta I have abandoned that pernicious view and have made the breakthrough to the Dhamma.”

“If, friend Yamaka, they were to ask you: ‘Friend Yamaka, when a bhikkhu is an arahant, one whose taints are destroyed, what happens to him with the breakup of the body, after death?’—being asked thus, what would you answer?”

“If they were to ask me this, friend, I would answer thus: ‘Friends, form is impermanent; what is impermanent is suffering; what is suffering has ceased and passed away. Feeling … Perception … Volitional formations … Consciousness is impermanent; what is impermanent is suffering; what is suffering has ceased and passed away.’ Being asked thus, friend, I would answer in such a way.”
SN 22.85

Why now do you assume 'a being'?
Mara, have you grasped a view?
This is a heap of sheer constructions:
Here no being is found.

Just as, with an assemblage of parts,
The word 'chariot' is used,
So, when the aggregates are present,
There's the convention 'a being.'

It's only suffering that comes to be,
Suffering that stands and falls away.
Nothing but suffering comes to be,
Nothing but suffering ceases.
SN 5.10

"Then, Bāhiya, you should train yourself thus: In reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. That is how you should train yourself. When for you there will be only the seen in reference to the seen, only the heard in reference to the heard, only the sensed in reference to the sensed, only the cognized in reference to the cognized, then, Bāhiya, there is no you in connection with that. When there is no you in connection with that, there is no you there. When there is no you there, you are neither here nor yonder nor between the two. This, just this, is the end of stress (suffering)."
Ud 1.10

Rebirth in Buddhism is not falsehood. It's not truth. It's just skillful means (upaya), a helpful tool. A middle way between falsehood and truth.