We're not talking trash about Hiashi. Quite the opposite. We're emphasising that a legitimate and conservative hokage recognised the religious legitimacy of the CoY. Therefore CoY is unquestionably legitimate, even among conservatives.
We are, in fact, talking trash about Hiashi. The paper-thin excuse of "we're talking about Hiashi-the-Hokage, not Hiashi-the-man" isn't one that can stand up to scrutiny. It's weaker than Hazou's "I was genjutsu-ed" excuse. And given that the Goketsu are a staunchly "liberal" clan, I think the fact that we're claiming a connection to one of the most traditional/bigoted Hokages is going to be enough of a red flag for people to realize that we're lying.
Again, it opens reprisals to talk about "Jiraiya-as-Hokage" in return. And Jiraiya was a world-famous smut author who led a nontraditional marriage, wherein both parties agreed not to be exclusive, sexually, to each other. While we might not give a damn, and the other "liberal" clans might not give a damn, Hinata could use that open secret to flay the Goketsu alive, politically speaking. It's bad enough the the Hagoromo, the leaders of Leaf's religious subculture, are on our case, but if we get the Hyuuga (an old, noble clan, as traditional as they come with all the power that comes with being a multigenerational major political force) on our case, I think we can safely write the Goketsu off as "politically irrelevant."
Besides, taking a dead man's reputation and dragging it through the mud like that doesn't rest well with me. Further, Hazou verbally reprimanded Noburi for mockingly saying that "Hinata should be glad her bastard of a father is dead" mere days after his death, and authorizing this seems like a major step back for his character.
To ordinary people they are. Most people never meet one. Even most jonin. Remember, even human preachers have convinced huge numbers of people that they were divine in nature, and they didn't have the advantage of being literally otherworldly.
I'd argue that magic is more widespread here, and that even if the civilians don't understand the minutiae, they'd still recognize "there's a mystical reason for this, and I've heard about legendary Summoners before [such as the Sannin]." So that loses much of the mystique and mystery that faith healers and cult leaders have in our mundane world.
When magical death beasts wander the world, and people who walking on water is a daily sight (in Leaf), the threshold for "divine" becomes all that much higher.
From what we've seen, it's buddhism wearing a toad texture pack. Also: the toad priest wants to convert people. Trust him to be good at his job.
I reread the update that was essentially a religious pamphlet, and I'll grant that missionaries are probably skilled at their jobs. But I'm not comfortable intentionally duping people into a religion that the player character doesn't even believe in. It feels too... slimy.
Note that my map has 31 known clans and doesn't seem to be close to comprehensive yet, so there's good odds a fair few of those clans either don't have scrolls (like perhaps the Leopards after they split from Cat) or their scrolls are chillin in a volcano or something.
Not to mention the Clans that might
have a summon scroll, but refuse summoners out of a lack of need. A summoner is like gravy, a nice perk to have, but ultimately a non-necessary one.