Sure if he is just using some kind of setting rationale to railroad, then yeah it could be. But if that isn't the reason, the players are just coming up against the limits of the setting itself, I don't think it is railroading.
This would be an odd NPC characteristic to create. So it is a slightly unusual example. But if you did have a character who had something they would never ever do, I don't know I would consider it railroading. We could certainly talk about whether it is good characterization. And it might depend on the system of course because some systems give things like social skills more control here. And there is a point where even the most staunch person might act (I wouldn't ever swim in the ocean, but if someone threatened to kill my family if I didn't, sure I am going to do it. But you are never going to persuade me through argument to swim in the ocean. Some just people won't do certain things unless the party physically forces them or coerces them (and coercion doesn't work on every single person, just ask Giles Corey)). Now if it is being done simply to obstruct the party, that is different. But staying true to an established character trait in an NPC, I wouldn't regard as railroading.
Is it reasonable in character for the NPC not to? Most people have things that they will not do.
Agree that if they would reasonably do that and the GM says no it can be railroading. In that case the GM is not making the world respond realistically.
Sure, there are some things people won't do. Although 1984, and I believe also Aristotle, present the opposite view, ie, that anyone can be broken if subjected to enough stress ("Do it to Julia!").
One way, in a RPG, to find out what a NPC is not prepared to do is to put it to the test of the mechanics (eg reaction rolls, or Persuader tests, or whatever else is the framework for the RPG in question).
If the GM decides in advance, and keeps it secret, then the fact that the GM's decision is "realistic" to their secret authored stuff doesn't make play not a railroad. A lot more has to be said about the workings of play than that - for instance, what actions might the players have reasonably declared that would then have obliged the GM to reveal the secret?
Who establishes that the character has that trait? Why is it established so?
Speaking for myself, I don't really care
why the GM decided that the NPC can't be persuaded to do <whatever>. Maybe they thought it was quirky? Maybe they thought it would make for a big reveal? Maybe they have modelled the NPC on some character they enjoyed reading about in a comic?
What I care about, as a player, is how I am able to play the game. If I can't reasonably judge the likely prospects of my action declarations achieving <this> or <that?, then I can't really play the game. And the more salient the action declaration is to the situations that the GM is presenting to me, the bigger an issue this becomes.
So, for instance, the GM deciding on a whim that the ground is too hard for me to dig a hole with my wooden shovel is probably harmless, if there's nothing really at stake in relation to shovel-digging, and I've just declared the action to establish a bit of colour for my PC. But the GM presenting a situation where there are action declarations that would be highly salient ways for the players to respond, while having secretly determined that some of those actions
will fail if declared, and not making this reasonably knowable by the players, is a completely different thing. The fact that the GM's secret decision also includes an explanation as to why the impossibility is "realistic" is neither here-nor-there.
Did you stop the character from attempting to persuade the NPC? If a character can never succeed (or fail depending on what is being attempted) unless it follows the predetermined path the GM has chosen then it's a railroad. A character can state that they climb a rainbow if they want but it's not going to work unless magic is involved.
There's no guarantee of a chance of success to any action a person in real life takes, I don't see why it would be any different in a game. Once again it looks like you're just adding things to the definition of what is required to play a sandbox because of your preference for a specific type of game.
From time to time I - the poster pemerton - persuade people of things, without using magic. It's a thing that can really happen. So the action
I try and persuade so-and-so to do <this thing that is the sort of thing a person in so-and-so's circumstances might be persuaded to do> is not comparable to
I climb the rainbow.
You ask,
why should there be a guarantee of a chance of success in a game? I think the answer is obvious: that's part of what it means to sit down and play a game! If I bring my wits to bear, and have a bit of luck, then I have a chance to win.
The GM secretly deciding that I
will fail in some meaningful action declaration, where I don't have a reasonable chance to work out in advance of the action declaration that it will be futile, is in my view not good game play. It's classic railroading!