In short, no, saying that there are some NPCs that simply can't be persuaded isn't wrong in any way. That's how the real world works, too. Some people can't be persuaded no matter how eloquent or powerful your argument is, sometimes simply because you're trying to persuade them.
That being said, you should also give them opportunities where a player who has invested their character into Persuasion and Charisma can shine and persuade people to do things. Just not all the time. I will usually write up some "important" things that NPCs believe in and can't be persuaded to violate (sometimes using the Background from 5e, for example), and then play the rest by ear.
For example, lets take the vestal virgin you mentioned above. If she's not an important NPCs to the plot, give him (whom I will call "Lothario" for clarity) a chance to destroy her vows and probably destroy any chance she has of remaining as a priestess (in other words, let the Lothario's player know that there are some
consequences if he succeeds). If he still wants to try it, let him roll, but use the fact that she would be hostile to this idea to raise her "mental defenses" against it. Since I run 5e, I use passive Insight to do so. As a priestess, she's probably got a decent wisdom, so lets say her passive Insight is 13 (10 + her Wisdom modifier). To get someone to sleep with you, you'd have to make the NPC's attitude towards the idea Helpful, and her starting attitude towards the idea is Hostile. For each step from Hostile to Helpful, add a +5 to her passive Insight; that means its Hostile -> Unfriendly -> Indifferent -> Friendly -> Helpful, so she'd have a passive Insight of 33 (13 + 20) to resist the Lothario's Persuasion attempts. Finally, our vestal virgin then would have to fail against the Lothario's persuasion a number of times equal to her Wisdom modifier before being persuaded, and she can only fail once per day (but our Lothario can get more than one success each day); you can give the Lothatio an extra success for each +5 over the NPC's passive Insight the Lothario rolls. I would probably also give him disadvantage if he was particularly crass in his attempt, too.
As a consequence of doing so, he and the party can no longer receive any healing from that priesthood at all, because of that player's actions (in the case of the vestal virgin, though, I'd have said "Well, the priestess actually curses you for the clumsy attempt at seduction. Roll a Wisdom save.") I chose to use this example because its the extreme and, unfortunately, common trope. I do not advocate attempting to seduce vestal virgins.
To prevent the slightly rape-y vibes of things above, I will provide some NPCs throughout the story that are "romance-able," just in case a player wants to do that sort of thing. Only twice has anyone taken up the opportunity, one being a gnome bard helping a tribal matriarch to overcome her sorrow, as it were, and the other actually ended up with the PC marrying the NPC and having triplets (yes, I had to write rules for pregnancy just for that).
Using it on another player character, though, is really dangerous for the health of the group. There's only one group that I've ever had where I would allow stuff like that, and even then I expect that they wouldn't. On the Pro side of things, it adds drama, and I like that; on the Con side, people get tetchy when you say, "Oh, your character has to do this thing." If you judge that your players are mature enough to handle the drama in-character, then use the above as a guide.