The first question is asking about this answer (in full):
All unenlightened beings suffer including scientists. I suppose the real question is whether scientists will ever realize the four noble truths. Unless there's a radical change in how they approach reality, I do not see that happening any time soon.
The real issue is that mainstream science still does not acknowledge that there is a mental aspect to the universe. They think of the mind as a byproduct of the brain. Any scientific research done based on that hypothesis will never lead to the understanding of the four noble truths.
The phrase you're asking about ("they think of the mind as a byproduct of the brain") seems to be an elaboration of the previous sentence ("The real issue is that mainstream science still does not acknowledge that there is a mental aspect to the universe"), and a bridge to the next sentence ("Any scientific research done based on that hypothesis will never lead to the understanding of the four noble truths").
I think the sentence wants to emphasise mental aspects (not physical aspects), as explained more-or-less explained in these comments (under a different answer):
If the scientists took the mental aspect of the universe seriously, today we would have very useful scientific theories on things like rebirth, Karma etc. – Sankha Kulathantille Mar 4 at 13:46
If the scientists took the mental aspect of the universe seriously When you write "the mental aspect", I guess that "mental aspect" includes ,"how we perceive it (sense-objects)", "how we feel about it (dissatisfaction)", and "how we react to it (anger or attachment)", and maybe "what's good (ethics, discipline, maybe kindness or selflessness too)". Is that what you mean by "the mental aspect" (which science should have studied), or did you mean something else? – ChrisW Mar 4 at 14:13
@ChrisW By the mental aspect, I mean 4 out of the 5 aggregates. Scientists only study 1. I.e. Rupa. Look how much they are missing. – Sankha Kulathantille Mar 4 at 14:15
So I think that answers that. Your question is "why does it matter if the mind is seen as a byproduct of the brain", and the answer appears to be that the brain is only a part of only one of the 5 skandhas, which is (I think, obviously) insufficient for the Buddhist endeavour.
In summary I don't think it's because it's relevant to "rebirth"; it's because it's too simplistic. And maybe too low-level: you can try to interpret everything (all activity) as physical/atomic, but IMO that is an inappropriate level in/at/from which to perceive feelings, ethics, and so on.
Yes you can take fMRIs of a brain in various states, but ...
As for the second question, "So, my second question is, does it really matter (in terms of holding the Right View) if the mind is neurologically originated or not?"
- I think it's OK to say that the mind has a "dependent origination" relationship.
- BUT "the mind" is complicated -- see e.g. What is the difference between Vijñāna, Manas and Citta?
- BUT "dependent origination" (the 12 nidanas) includes more than only "mind and brain" (i.e. it's more complicated than that)
- BUT tradition includes "immaterial (formless) realms", and inhabitants thereof (devas), and any claim that "there is no mind without brain" may appear to contradict that.
- BUT "the mind originates in the brain" isn't taught (historically orthodox), isn't included in any definition of Right View, and maybe isn't a soteriological doctrine -- which prefers to teach that mental phenomena are mind-made (not that mind is matter-made)
As a scientist perhaps I might say that "the theory that 'the mind originates in the brain' is a model which seems to explain various phenomena".
But maybe it's not the best (or right) model, to explain the kinds of observation that are the subject of Buddhist doctrine.
To answer the question with a rhetorical question, do you think you can arrive at, for example, a neurological understanding of the four noble truths? Can other people? Is it that doctrine that's readily apparent, inviting inspection, maybe self-evident etc.?
Again I don't think it's necessarily to do with "rebirth", only that assuming that "the physical is all there is" isn't the right perspective from which to understand Buddhist doctrine or practice.