...we should at least hope for additional evidence, better controlled
experimentation, showing that it is possible to recover memories that
are not encoded in neural tissue, that it is possible to sustain
consciousness in organisms that lack nervous systems, that it is
possible for mental causation to cross time and space and alter
Negative experiments along these lines are legion, though they rarely
find their way to the front page of your local newspaper, since nobody
has any reason to promote them. One can find mention of them in places
like Skeptical Inquirer magazine, or outlined at websites like the
Skeptic’s Dictionary or Quackwatch.
It is for reasons such as these that any contemporary, scientifically
informed Buddhist practice should reject belief in rebirth and its
associated kammic causation.
Quoted above is from the link you attached with regards to Secular Buddhists. In short, the set of arguments is... because we can't experimentally recover memories that are not encoded in neural tissue, etc.. it follows that rebirth is false. That right there is a pure materialist view, similar to the Charvakas idea which the Rinpoche said has no place in Dharma.
Following the same analogy, the Secular Buddhist will not find a different neural tissue memory imprint representing intention between the monk approaching a certain nun and the lover.
So the danger in the materialistic view is that the modifiability of Kamma (intention) is denied and without that, there is no liberation from the samsaric cycle of suffering.
Quoted below is from Kamma and its Fruit by Nyanaponika TheraNyanaponika.
However, a scientist's view is not finalized, a scientist doesn't start with a premise that everything is material or that the equipment he/she has can recover everything knowable thus will not reject the unproved rebirth idea or any unproven idea for that matter. That is why I think Rinpoche says a scientist could be a vessel for the Dharma.
Most writings on the doctrine of kamma emphasize the strict lawfulness
governing kammic action, ensuring a close correspondence between our
deeds and their fruits. While this emphasis is perfectly in place,
there is another side to the working of kamma — a side rarely noted,
but highly important. This is the modifiability of kamma, the fact
that the lawfulness which governs kamma does not operate with
mechanical rigidity but allows for a considerably wide range of
modifications in the ripening of the fruit.
If kammic action were always to bear fruits of invariably the same
magnitude, and if modification or annulment of kamma-result were
excluded, liberation from the samsaric cycle of suffering would be
impossible; for an inexhaustible past would ever throw up new
obstructive results of unwholesome kamma. Hence the Buddha said:
"If one says that in whatever way a person performs a kammic action,
in that very same way he will experience the result — in that case
there will be no (possibility for a) religious life and no opportunity
would appear for the complete ending of suffering.
"But if one says that a person who performs a kammic action (with a
result) that is variably experienceable, will reap its results
accordingly — in that case there will be (a possibility for) a
religious life and an opportunity for making a complete end of
— AN 3.110