I struggled with this with my players, but as I've played as a player more, I've started to see things from their perspective, and made some changes to the way I DM which seem to have helped.
As a DM, my main concern was for the overarching story, but as I player I just wanted to be able to make decisions. Choosing what breakfast to order or which clothes to buy was as much fun as interrogating an NPC or having a big combat. I realised I'd been choking out these decisions when I DMd because they messed with my plan. Trying to remember that the players have the most fun when they get to make decisions has really helped ease some of these tensions. Here's some of the things I'm now trying to do more.
The players find the information, not the DM
At the beginning of the side quest, a local busy-body sidles up to them at a bar to gossip and they declare that this person is some kind of trickster.
I had this happen a lot. One player was sure a carriage driver was leading them into an ambush, and an innkeeper wanted to sacrifice them in a ritual. It took several out-of-game conversations for me to realise that they were actually right. Those NPC did have an ulterior motive. The motive was that I wanted to explain the backstory, but it was still there. What's more, because I was role-playing a conversation, I'd implied this was a decision-making opportunity. Except they were really cut-scenes, and the only choice was to keep pressing X until I was done. The players were suspicious, but didn't have any meaningful choices, so it's not surprising they just said "no".
Then one session I had some thieves steal something right in front of them. Suddenly, one player was super engaged and kept talking to the thieves and get more information out of them, even though it was just supposed to be a simple fight. I'd (accidentally) presented it as an encounter, not a cut-scene, and they lapped it up. Likewise, my players avoided a big dragon fight (that I'd spent ages planning) to instead spend an hour discussing a piece of lore I thought I'd made obvious. I came away really upset with how boring the session had been, but I was told only this week that it was one player's favourite session. They got to spend the entire time debating with the rest of the party, and making decisions about how they would handle things, rather than just listening to me tell them where to go next.
It seems your players did the same thing: they didn't want to information when just talking to an NPC, but when an actual encounter showed up they suddenly wanted the information. Rater than being frustrated, I've tried to learn from this.
Now I try to use the "encounter" approach in all my scenes. Rather than have someone come up to them, try making two guy sit in the corner looking suspicious. They mutter something about "treasure", but look away as soon as you see them. If the players want to be suspicious of everything, give them something to be suspicious about! It also lets them actually make decisions - the fun bit of the game. Do they want to stealthily eavesdrop? Buy them a drink and make friends? Start a tavern brawl?
Of course, sometimes you really do need the players to just learn some information. In which case, I tend to find not dressing it up as a role-playing situation is most effective. Hand them a physical IRL letter from the town guard asking for their help. Tell the players "as a the barman pours you a drink, he tells you that about some kind of underground tomb nearby". Give them the information they need, and then move as quickly to the next point where they can make decisions - even if that's just what drinks they order.
The players decide what to do, not the DM
So, instead of talking to the local noble (one of the captives) about what is going on, they pump nobodies for information they clearly would not have.
Being a player, I realised that even when I wrote encounters, I still wasn't giving the players decisions. I'd already decided which actions were "good", and the players would only get the information if they did those actions.
So now when I'm writing encounters, I'm trying hard not pre-decide the solutions. If the players want to talk to the nobodies, there's no reason that one of them couldn't have worked in the palace kitchens, or overheard the nobles talking in the camp. I'm not saying I'd let every action work, but I haven't decided in advance what the one sensible action is going to be.
This was proven recently when I DMd a one-on-one session that was completely spur of the moment. I pulled a half-written one-shot out and we just dove straight in. I had no idea what the "good" actions were, because I hadn't had time to think about what they might do. It was, without question, the best session I've ever DMd, because when I asked "what do you do?", I actually meant it.
After giving them a chance to decide what to do (they want to stay in the comfortable bar)
I'm also learning to relish this sort of thing. The players have expressly told you what they're going to enjoy. Spend the next ten minutes asking them what they order at the bar. Let them roll some Consitution checks to see if they can outdrink each other. Let them insult a tipsy orc, who decides to insult them back, and they have a friendly banter match. Sure, it doesn't progress the story, but it gives the players a series of silly decisions to make, and that's the thing they find fun. And then when they're all laughing with the drunk orc, have him mention the secret tomb...
The DM asks for dice rolls, not the players
No insight checks or perception or anything, just the simple fact that this person is trying to talk to them is enough information to know this is a trap.
Players don't ask for checks, they describe what they do. The DM decides when that requires a dice roll.
This took me a long time to get my head around in my games, but your players did call for an insight check. Here's how the PHB describes Insight:
Insight. Your Wisdom (Insight) check decides whether you can determine the true intentions of a creature, such as when searching out a lie or predicting someone’s next move. Doing so involves gleaning clues from body language, speech habits, and changes in mannerisms.
Your players took "clues from body language" ("the simple fact this person is trying to talk to them") and used them to "determine the true intentions of a creature" ("this is a trap"). They didn't use the words "insight check", but they shouldn't have to. The players describe their actions, and then DM decides whether to ask for a dice roll. Realising this changed the way I handle dice rolls, and it makes my players much more engaged with the world. They can focus on what their characters are doing, and as soon as they start to jump to the wrong conclusions, I can use a check (or just a passive) to get them on the right lines again.
They are convinced that this is a trap without any evidence. That the townsfolk will transform into zombies (yes, literally) and they will all be killed.
You can use the same trick here. As soon as the players start saying this, you can either call for an arcana check, or just tell them they (passively) don't sense any magic.
Usually DM advice is to make the answers a bit vague, especially for low rolls ("He doesn't seem to be lying", "you don't notice any magic"), but I've found that isn't helpful for naturally suspicious new players. Being very clear ("Even with a roll of 6, you are certain he's not lying, but you can't tell his actual motivations") has tended to produce better results for me, because the players are much clearer about what's going on. The same may be true when the players tried to convince the townsfolk to join. Clearly saying "succeed a DC15 persuasion check, you'll have advantage on your attacks as the crowd help" is going to make it a lot easier for the players to decide whether it's worth spending an action on.
Those are some of the things that I've tried to change, and it seems like my sessions are running better now. Hopefully some of these help you to! For what it's worth, I've learned some of this advice from The Angry GM's True Game Mastery series, which I've found very helpful if you're willing to put up with the "angry" persona.