Recently I had my players read through the Investigator's Handbook in hope that they get familiar with the basic rules and will be more devoted to the game.
Unfortunately, they found this sentence in Chapter 9: Advice for Players
After that, they recall the sentence each time I tell them they are faced with some cultist and would always end up laughing. Certainly it ruined the tension and the horrific atmosphere.
So, is it intended by the rule to allow such strange behavior?
I myself find persuading some cultist during battle or confrontation really, really ridiculous.
They're not the brother...says who?
Yeah, fast talk isn't wrong either. It just depends on what you're trying to achieve. I think the disconnect we're having here is that you're assuming a context: the PC arbitrarily selects some faceless fodder enemy in robes and claims to be their sibling for some momentary advantage. In that case I'd agree with you and go a lot further--I wouldn't allow a roll at all. People are in general aware of their immediate family, and you're right that some cultist picked out of a bunch is not likely to care about anything they have to say or be reasonable at all.
But the context isn't set. It's wide open! It only sounds outrageous because it's laid bare with no context; you could build a hefty plot spanning multiple sessions around that one line. There are reasons and occasions to use Persuade on a cultist--they aren't inherently faceless fodder enemies. The GM could create a specific cultist, maybe the head of the cult or an influential member whose backstory includes a long-lost sibling. Maybe they need them for something specific, and they're attempting to locate them. The PCs can learn about this, and a particular PC could attempt to pose as the long-lost sibling, or could in fact be the sibling.
It's cool to weave PC backstories into the plot sometimes, and there's a solid basis in Lovecraftian fiction for characters to discover unfortunate familial ties and suffer for them. Whatever you decide to do, just make sure the PC is suffering. I mean, I'm not trying to tell you what to do, it would just make me happy to hear that the PCs are suffering. 😁