The first part, "bold and confident claims", sounds like it might be associated with doctrines about "stream-entry".
I think that one of the characteristics of stream-entry is "confidence" -- for example SN 55.40
a disciple of the noble ones is endowed with verified confidence
Whether that confidence is justified or deluded is another question -- which I think is a well-known problem/question -- i.e. "how can you tell whether you are or whether someone else is a stream-winner?"
Further to that subject, this answer says that a stream-winner might have conceit -- but only "true" conceit.
One of the way to avoid that problem -- I hope -- is to cite references. For example "a confident claim about what Buddhism is or isn't" might be accompanied or supported by a reference to a Buddhist sutta -- then the claim of whether something is "Buddhist" might rest of whether it is (accurately) based on "a Buddhist sutta".
Pali suttas begin with ...
so i have heard.
evaṃ me sutaṃ—
... which I like.
After a while -- after you learn some "Buddhism" -- you may or may not need or want to ask for references, when someone says something about Buddhism without citing a reference -- because you might recognise which sutta or other doctrine supports what they are saying.
Then there's also a matter of, whether you can "verify" a doctrine based on your own experience -- because the dhamma is said to be:
... well declared by the Bhagavā:
visible here and now, immediate,
inviting to come and see, effective,
to be individually ascertained by the wise.
Another solution is to find a teacher of whose teaching you are confident.
The second part, "anything contrary to their view is asserted to be simply wrong", sounds more questionable to me. I think a lot of suttas warn that arguing might be papanca etc.
Three passages in the discourses — DN 21, MN 18, and Sn 4.11 — map the causal processes that give rise to papañca and lead from papañca to conflict. Because the Buddhist analysis of causality is generally non-linear, with plenty of room for feedback loops, the maps vary in some of their details. In DN 21, the map reads like this:
the perceptions & categories of papañca > thinking > desire > dear-&-not-dear > envy & stinginess > rivalry & hostility
In Sn 4.11, the map is less linear and can be diagrammed like this:
perception > the categories of papañca
perception > name & form > contact > appealing & unappealing > desire > dear-&-not-dear > stinginess/divisiveness/quarrels/disputes
In MN 18, the map is this:
contact > feeling > perception > thinking > the perceptions & categories of papañca
The third part, "developing contentment with the uncertainty of reality", sounds like basic right speech -- AN 10.176
"And how is one made pure in four ways by verbal action?
"There is the case where a certain person, abandoning false speech, abstains from false speech. When he has been called to a town meeting, a group meeting, a gathering of his relatives, his guild, or of the royalty, if he is asked as a witness, 'Come & tell, good man, what you know': If he doesn't know, he says, 'I don't know.' If he does know, he says, 'I know.' If he hasn't seen, he says, 'I haven't seen.' If he has seen, he says, 'I have seen.' Thus he doesn't consciously tell a lie for his own sake, for the sake of another, or for the sake of any reward. Abandoning false speech, he abstains from false speech. He speaks the truth, holds to the truth, is firm, reliable, no deceiver of the world.
"Abandoning divisive speech he abstains from divisive speech. What he has heard here he does not tell there to break those people apart from these people here. What he has heard there he does not tell here to break these people apart from those people there. Thus reconciling those who have broken apart or cementing those who are united, he loves concord, delights in concord, enjoys concord, speaks things that create concord.
"Abandoning abusive speech, he abstains from abusive speech. He speaks words that are soothing to the ear, that are affectionate, that go to the heart, that are polite, appealing & pleasing to people at large.
"Abandoning idle chatter, he abstains from idle chatter. He speaks in season, speaks what is factual, what is in accordance with the goal, the Dhamma, & the Vinaya. He speaks words worth treasuring, seasonable, reasonable, circumscribed, connected with the goal.
"This is how one is made pure in four ways by verbal action."
Finally, all dhammas (including the dhamma) are supposed to be "non-self".
And Buddhists do I think "cherish" the dhamma.
So it may be "dhamma-cherishing" rather than "self-cherishing".
But one of the modern teachers warned against "Spiritual materialism" -- I don't know what exactly that might correspond to in the earlier doctrines -- and I haven't even read what "spiritual materialism" means exactly, I think it means something like, an egoistic tendency to want to accumulate spiritual attainment in the same way that other people like to accumulate material things like fame or fortune.
So, I guess, yes, it's sensible to be a bit sceptical.
I think there are people, though, who will teach the doctrine carefully and maybe step-by-step and also so on -- AN 5.159
It's not easy to teach the Dhamma to others, Ananda. The Dhamma should be taught to others only when five qualities are established within the person teaching. Which five?
- The Dhamma should be taught with the thought, 'I will speak step-by-step.'
- The Dhamma should be taught with the thought, 'I will speak explaining the sequence [of cause & effect].
- The Dhamma should be taught with the thought, 'I will speak out of compassion.'
- The Dhamma should be taught with the thought, 'I will speak not for the purpose of material reward.'
- The Dhamma should be taught with the thought, 'I will speak without hurting myself or others.'(note)
It's not easy to teach the Dhamma to others, Ananda. The Dhamma should be taught to others only when these five qualities are established within the person teaching.
(note) According to the Commentary, "hurting oneself" means exalting oneself. "Hurting others" means putting other people down.