I wanna smack the whole lot of them. I'll normally defend characters being "stupid" or "illogical" because teenagers are going to be stupid and illogical, but this is a level of rudeness that really deserves repurcussion. Even if the MC is an outcast and looked down on for his antisocial (and self-sabotaging) personality, you do not crowd around a young child like they're a brand new puppy! Especially when they're clearly getting stressed about it!
....That having been said, it does make sense for the students to be suspicious and not take him at face value. Aoyagi has, as said earlier, actively put himself on the outs with just about the whole class, and him being so close to Emma (despite having "just met her" supposedly) would definitely feel off to me as well. If anything them flipping immediately just on Charlotte's word is its own kind of stupid, but... Well, idol culture + being Emma's older sister = "well obviously she's know better than any of us."
Still wanna smack 'em though.