He hates the Shield Hero because he fought a war with Siltvelt, a country that worships him. Because of such, he unjustly villainizes Naofumi, simply because he bares the role, unwillingly; and helps Malty with her lies, even "confiscating" his Earth clothes despite the fact they are Naofumi's property.

Why does malty Melromarc hate Naofumi?

She seems to have sided with him purely because of his good looks. She easily convinced Motoyasu of falsely claiming Naofumi of having a "brainwashing shield", by which he supposedly brainwashed the people, kidnapping the second princess and killing Ren and Itsuki.

Why does MYNE hate the shield hero so much?

She is a believer of the Religion of the Three heroes. The official religion of the Nation. Such religion deems the Shield Hero as a demon. Hence she constantly is in contact with the Pope of the Church and trying to taint Naofumi's reputation behind the scenes.