If there are any Buddhists who hold the view that no beings are reborn, they are certainly right in that there is no absolute thing as a being or self, as Bhikkhuni Vajira reaffirmed to Mara in SN 5.10:
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.
However, this does not mean that there are no beings at all. It simply means that "being" is a convention to denote the presence of the five aggregates occurring together. There is no absolute entity called being that exists standalone and independently of everything. The same thing applies to the self. There is no standalone or independent thing called self, but the self arises when the five aggregates operate together in the same way music arises when different parts of a violin work together to produce music.
This does not mean that suffering ends at death. Suffering only ends with Nibbana. Suicide is not a means to end suffering.
The fact that suffering does not end with death is evidenced in so many suttas, including MN 60, MN 36, DN 15, SN 15, MN 19, MN 57, SN 44.9, MN 83, DN 2, Dhp 153-154.
Some secular Buddhists claim that rebirth is a moment-to-moment change in one's state of mind, but it does not refer to physical rebirth. However, in MN 19, the Buddha clearly stated that with the break-up of the body, there are beings who are reborn elsewhere:
"When the mind was thus concentrated, purified, bright, unblemished,
rid of defilement, pliant, malleable, steady, & attained to
imperturbability, I directed it to the knowledge of the passing away &
reappearance of beings. I saw — by means of the divine eye, purified &
surpassing the human — beings passing away & re-appearing, and I
discerned how they are inferior & superior, beautiful & ugly,
fortunate & unfortunate in accordance with their kamma: 'These beings
— who were endowed with bad conduct of body, speech & mind, who
reviled the Noble Ones, held wrong views and undertook actions under
the influence of wrong views — with the break-up of the body, after
death, have re-appeared in the plane of deprivation, the bad
destination, the lower realms, in hell. But these beings — who were
endowed with good conduct of body, speech, & mind, who did not revile
the Noble Ones, who held right views and undertook actions under the
influence of right views — with the break-up of the body, after death,
have re-appeared in the good destinations, in the heavenly world.'
Thus — by means of the divine eye, purified & surpassing the human — I
saw beings passing away & re-appearing, and I discerned how they are
inferior & superior, beautiful & ugly, fortunate & unfortunate in
accordance with their kamma.
Also DN 15 clearly shows rebirth into a human womb from the context of dependent origination (also see this answer):
"'From consciousness as a requisite condition comes name-and-form.'
Thus it has been said. And this is the way to understand how from
consciousness as a requisite condition comes name-and-form. If
consciousness were not to descend into the mother's womb, would
name-and-form take shape in the womb?"
"No, lord."
"If, after descending into the womb, consciousness were to depart,
would name-and-form be produced for this world?"
"No, lord."
"If the consciousness of the young boy or girl were to be cut off,
would name-and-form ripen, grow, and reach maturity?"
"No, lord."
"Thus this is a cause, this is a reason, this is an origination, this
is a requisite condition for name-and-form, i.e., consciousness."
Another good sutta is SN 44.9 which states:
And at the moment when a being sets this body aside and is not yet
reborn in another body, what do you designate as its sustenance then?"
"Vaccha, when a being sets this body aside and is not yet reborn in
another body, I designate it as craving-sustained, for craving is its
sustenance at that time."
Here's another - Dhammapada 400:
Akkodhanam vatavantam
silavantam anussadam
dantam antimasariram1
tamaham brumi brahmanam
Verse 400: Him I call a brahmana, who is free from anger, who
practises austerity, who is virtuous and free from craving, who is
controlled in his senses and for whom this body (i.e., existence) is
the very last.
Footnote 1. antimasariram: lit., one who has the last body. This is his last body because he will not be reborn; he is an arahat.
And another - SN 12.19:
The Blessed One said this:
“Bhikkhus, for the fool, hindered by ignorance and fettered by
craving, this body has originated. For the fool that ignorance has not
been abandoned and that craving has not been utterly destroyed. For
what reason? Because the fool has not lived the holy life for the
complete destruction of suffering. Therefore, with the breakup of
the body, the fool fares on to another body. Faring on to another
body, he is not freed from birth, aging, and death; not freed from
sorrow, lamentation, pain, displeasure, and despair; not freed from
suffering, I say.
So, why don't some Buddhists believe in kamma and rebirth?
Well, the answer is that they hold the wrong view of annihilationism, as stated in DN 1 (below). Most of them hold the view of physicalism, that nothing exists beyond the physical world, just as flat-Earthers think the Earth is flat because it apparently appears so to their limited senses.
"There are, bhikkhus, some recluses and brahmins who are
annihilationists and who on seven grounds proclaim the annihilation,
destruction, and extermination of an existent being. And owing to
what, with reference to what, do these honorable recluses and brahmins
proclaim their views?
"Herein, bhikkhus, a certain recluse or a brahmin asserts the
following doctrine and view: 'The self, good sir, has material form;
it is composed of the four primary elements and originates from father
and mother. Since this self, good sir, is annihilated and destroyed
with the breakup of the body and does not exist after death, at this
point the self is completely annihilated.' In this way some proclaim
the annihilation, destruction, and extermination of an existent being.
"To him another says: 'There is, good sir, such a self as you assert.
That I do not deny. But it is not at that point that the self is
completely annihilated. For there is, good sir, another self — divine,
having material form, pertaining to the sense sphere, feeding on
edible nutriment. That you neither know nor see, but I know it and see
it. Since this self, good sir, is annihilated and destroyed with the
breakup of the body and does not exist after death, at this point the
self is completely annihilated.' In this way others proclaim the
annihilation, destruction, and extermination of an existent being.
"To him another says: 'There is, good sir, such a self as you assert.
That I do not deny. But it is not at that point that the self is
completely annihilated. For there is, good sir, another self — divine,
having material form, mind-made, complete in all its limbs and organs,
not destitute of any faculties. That you neither know nor see, but I
know it and see it. Since this self, good sir, is annihilated and
destroyed with the breakup of the body and does not exist after death,
at this point the self is completely annihilated.' In this way others
proclaim the annihilation, destruction, and extermination of an
existent being.
"To him another says: 'There is, good sir, such a self as you assert.
That I do not deny. But it is not at that point that the self is
completely annihilated. For there is, good sir, another self belonging
to the base of infinite space, (reached by) the complete surmounting
of perceptions of material form, by the disappearance of perceptions
of resistance, by non-attention to perceptions of diversity, (by
contemplating) "Space is infinite." That you neither know nor see, but
I know it and see it. Since this self, good sir, is annihilated and
destroyed with the breakup of the body and does not exist after death,
at this point the self is completely annihilated.' In this way others
proclaim the annihilation, destruction, and extermination of an
existent being.
"To him another says: 'There is, good sir, such a self as you assert.
That I do not deny. But it is not at that point that the self is
completely annihilated. For there is, good sir, another self belonging
to the base of infinite consciousness, (reached by) completely
surmounting the base of infinite space (by contemplating):
"Consciousness is infinite." That you neither know nor see. But I know
it and see it. Since this self, good sir, is annihilated and destroyed
with the breakup of the body and does not exist after death — at this
point the self is completely annihilated.' In this way some proclaim
the annihilation, destruction, and extermination of an existent being.
"To him another says: 'There is, good sir, such a self as you assert.
That I do not deny. But it is not at that point that the self is
completely annihilated. For there is, good sir, another self belonging
to the base of nothingness, (reached by) completely surmounting the
base of infinite consciousness (by contemplating): "There is nothing."
That you neither know nor see. But I know it and see it. Since this
self, good sir, is annihilated and destroyed with the breakup of the
body and does not exist after death — at this point the self is
completely annihilated.' In this way some proclaim the annihilation,
destruction, and extermination of an existent being.
"To him another says: 'There is, good sir, such a self as you assert.
That I do not deny. But it is not at that point that the self is
completely annihilated. For there is, good sir, another self belonging
to the base of neither perception nor non-perception, (reached by)
completely surmounting the base of nothingness (by contemplating):
"This is the peaceful, this is the sublime." That you neither know nor
see. But I know it and see it. Since this self, good sir, is
annihilated and destroyed with the breakup of the body and does not
exist after death — at this point the self is completely annihilated.'
In this way some proclaim the annihilation, destruction, and
extermination of an existent being.
"It is on these seven grounds, bhikkhus, that those recluses and
brahmins who are annihilationists proclaim the annihilation,
destruction, and extermination of an existent being. Whatever recluses
or brahmins proclaim the annihilation, destruction, and extermination
of an existent being, all of them do so on these seven grounds or on a
certain one of them. Outside of these there is none.