Discernment or blind belief? Recently I was chatting with some Christian friends and we were recollecting some of Jesus' teachings - I, particularly, specified a couple aspects of the New Testament that were downright absurd; one is resurrection: one group of Christians believe Christ had actually raised from the dead, and the other that it was a metaphor. The first view is obviously non-scientific, and one might actually argue it makes no sense.
I have been reading the nikayas myself and although I have found them to be beautiful, I cannot avoid detecting leftovers of Hinduism and absurdity in Buddha's sayings - if taken literally. I have already asked a question about the absurdity of interpreting rebirth literally, and was satisfied with Buddhadasa Bikkhu's view that it should be interpreted metaphorically - even though Buddha explicitly said that rebirth also happened after death (references can be found in the linked question). I now have read more suttas and am very dislocated with regards to many passages. I list some of them below.
Buddha affirms ugliness is a direct consequence of past lives (MN 135):

There is the case, where a woman or man is ill-tempered &amp; easily upset; even when lightly criticized, he/she grows offended, provoked, malicious, &amp; resentful; shows annoyance, aversion, &amp; bitterness. Through having adopted &amp; carried out such actions, on the break-up of the body, after death, he/she reappears in the plane of deprivation... If instead he/she comes to the human state, then he/she is ugly wherever reborn.

Buddha affirms conception is only possible with the presence of a lesser metaphysical creature to be reborn in the foetus (MN 93):

&quot;'Do you know how there is the descent of an embryo?'
&quot;'Yes, master, we know how there is the descent of an embryo. There is the case where the mother &amp; father have come together, the mother is fertile, and a gandhabba [the being about to be reborn] is standing present. The coming together of these three is the descent of the embryo.'

Buddha affirms that Dhamma practise will turn a person into, let's face it, some sort of superman (DN 2):

With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to the modes of supranormal powers. He wields manifold supranormal powers. Having been one he becomes many; having been many he becomes one. He appears. He vanishes. He goes unimpeded through walls, ramparts, and mountains as if through space. He dives in and out of the earth as if it were water. He walks on water without sinking as if it were dry land. Sitting cross-legged he flies through the air like a winged bird. With his hand he touches and strokes even the sun and moon, so mighty and powerful. He exercises influence with his body even as far as the Brahma worlds.

If taken metaphorically, the last quote can make sense. The first and second are fruits of a mind that was born in the VI BCE, before the discovery of genetics and physiology.
A previous question has answers that say that to be a Buddhism a person has to have &quot;unwavering faith in Buddha&quot;. Does that mean that to become a Buddhist I must give hand of science and start believing nonsense like this? Is it part of being a Buddhist believing everything the Buddha said is true, or must I be discerning and throw away things that are now know to be false?
I have already understood that the role of Buddha is taken to be showing mankind the Four Noble Truths and the Eightfold Path. These do make sense for me, completely... But I'm stuck with those esoteric aspects of Buddhism.
Sometimes, the Buddha puts in check any blind faith his listeners might have about himself or the dhamma itself. A notorious sutta here is the  Cūlahatthipadopama Sutta, where he explains that the reasons for Pilotika to believe the enlightenment of the Buddha are insufficient to have him to state it to surely. In this case, he uses the simile of the elephant's footprint:


  “Brahmin, suppose an elephant woodsman were to enter an elephant wood and were to see in the elephant wood a big elephant’s footprint, long in extent and broad across. A wise elephant woodsman would not yet come to the conclusion: ‘Indeed, this is a big bull elephant.’ Why is that? In an elephant wood there are small she-elephants that leave a big footprint, and this might be one of their footprints. [...]


On other occasion, the Buddha approaches people who are not his followers and starts his speech telling them to be careful about the reasons one believes in something. Such is the famous Kesaputtiya sutta also known as the Kālāma Sutta:


  The Kesaputtiya Sutta is a classic discourse on Buddhist epistemology, that is, theory of knowledge, or an investigation into what constitutes valid knowledge and what does not. [...] A remarkable feature of the Kesaputtiya Sutta is the comprehensive manner in which it covers the range
  of human knowledge and experience, that is, the cognitive, the conative, the affective and the spiritual. The cognitive aspect of the Sutta is covered by the Buddha’s reassuring that the Kālāmas have the right to doubt what is doubtworthy and exhorting them on the 10 doubtworthy points.
  
  -- Piya Tan


Another sutta that deals with the acceptance of views and how this acceptance affects one's life is the Apaṇṇaka sutta, which Thanissaro Bhikkhu has translated as "a safe bet".


  One of these means [the Buddha resorted to] was the pragmatic argument, which differs from empirical arguments as follows. An empirical argument presents facts that logically imply that A must be true or false. A pragmatic argument focuses not on the facts related to A, but on the behavior that can be expected from a person who believes or rejects A.
  
  The Buddha's main pragmatic argument is that if one accepted his teachings, one would be likely to pay careful attention to one's actions, so as to do no harm. This in and of itself is a worthy activity regardless of whether the rest of the path was true. 
  
  When applying this argument to the issue of rebirth and karmic results, the Buddha sometimes coupled it with a second pragmatic argument that resembles Pascal's wager: If one practices the Dhamma, one leads a blameless life in the here-and-now. Even if the afterlife and karmic results do not exist, one has not lost the wager, for the blamelessness of one's life is a reward in and of itself. If there is an afterlife with karmic results, then one has won a double reward: the blamelessness of one's life here and now, and the good rewards of one's actions in the afterlife. These two pragmatic arguments form the central message of this sutta.
  
  -- Thanissaro Bhikkhu 


Finally, the Brahmajāla Sutta is an important discourse that exposes what the Buddha calls wrong views. It is a great source to understand indirectly what the Buddha approves to be knowledge -- by understanding how he exposes faulty inquiries of many different kinds.



So, I hope suttas like these clarify that Buddhism does not demand one's blind faith on any matter. Not only it doesn't demand blind faith, but assertions about the Dhamma that have not being actually made known by those who proclaim it are subject to criticism (if the simile of the elephant's footprint is at all relevant).

Of course, all buddhists aiming at the goals of Buddhism have to have some faith in things beyond their current reach. That the goal (end of suffering) is reachable, and that the path presented truly moves one toward that goal  are two obvious instances.

But this faith is the very same faith one has on math class, or say, rock climbing class: faith that the teacher knows his trade, that it's possible for you to learn it, and that by the end of the course, you will know it. There's then a gradual "substitution" of that faith by knowledge; as you learn, the more confident in the path and teacher you become. This is daily activity, we all do it, and in Buddhism is not different.

Now, consider the situation were the student really, really needs the class and ponders over the options carefully. Then, the "unwavering faith in the Buddha" is just this: without fully trusting the teacher, one comes to believe one won't learn the class as well as one expects, or worst, one may think they are not safe under the care of the teacher. So right there the motivation ends and one abandons that class. That is why this strong confidence is required for those truly dedicated to realize the attainments declared by the Buddha, otherwise they will doubt the very possibility of it and abandon the training.

Strong as it may be, however, the faith is provisional. It's mere confidence. And if the suttas above are at all important, they point to the very same attitude that mature scientists show: that we should never assert things we don't know as true if we have not come to know them as true -- we can always say "according to the suttas", but that's different than saying "this is true".

On the other hand, no one interested in finding truth should discard nonsense because it's perceived as nonsense. For one example, for centuries the idea that the earth moves around the sun, and that the earth is actually spinning was nonsense (to our senses, it still is: I don't feel I'm spinning at all, and I can clearly see the sun moving around).

No one should also believe in science for so many reasons. One of them, is that science is supposed to be known, not believed in (that was the whole point of the scientific revolution centuries ago) -- this is quite aligned with Buddhism. 

But the point is that rebirth has never been under sufficient scientific scrutiny, enough to yield any conclusive information. The same can be said about the brain. That doesn't make the brain "non-scientific".

So, throw away what is false, yes. But one better be cautious so one is not mistaken about it -- since we usually are not cautious and we usually are mistaken.

Last but not least, there are other interpretations of the quotes you provided, and many people believe rebirth in the suttas to be either a mis-interpretation or that it's presence in the texts are due to other reasons. Secular Buddhism, for example, is one branch that takes the so-called supernatural elements with grain of salt.

But many monks are actually agnostic about rebirth or put this subject aside. Ajahn Brahmali from the forest tradition thinks that this is appropriate middle way on this matter.