Yes, Goths typically hate Emos.
This is especially true amongst older Goths who are bitter that they are now impotent and irrelevant. Fans of band’s like Joy Division will be deliberately hostile to My Chemical Romance fans simply because they are jealous that MCR can produce music that’s worthwhile, funny and not totally fucking shit.
Some Goth’s will even deny the existence of Emo, before embarking on an “Emo Hit” downtown, where they’ll pack a car full of their Goth friends, scouring the street for a legitimate Emo target to egg to death.