Naru trusts her on personal matters; as shown when he asks Mai to keep his spoon-bending activity a secret, early on in the series.
He always enjoyed the look on Mai's face when he surprised her.
Mai respects John's talent as an exorcist.
Setting them onto a tray, she placed three teaspoons beside them, and made her way down the hallway to where Lin was no doubt hunched over his computer in his usual way.
None the less, she rushed to the best of her current ability, trying to get to work before she was even later.
In the beginning, Mai seems to have no problem working with these other experts; however, she does berate them for not admitting their mistakes and doubting Naru's abilities.