Well there's the case of druidic worship. While the worship of celtic deities wasn't prohibited and often they were combined with the roman religion as epithets of their own pantheon and the concept of Interpretatio romana. But Romans were weary of the Druids themselves themselves as religious leaders. Firstly because they were associated with human sacrifice in the roman mind and propaganda which was considered barbaric. Secondly perhaps because they were associated with encouraging uprisings against roman rule. A number of emperors made efforts to discourage or stamp out Druidism with Claudius making a particular effort, attacking Anglesey in Wales as one of the last major holy sites of Druidy and looking to stamp out druidic practices in Roman controlled territories.

There were a few other examples, mainly mystery cults like Jupiter Dolichenus which was attacked for political reasons. When Maximinus I came to power he identified the Dolichenus cult as being a suitable target. It came from the east of the empire in the general region of Syria, as the Severus', the proceeding dynasty had. PLus the last of the old dynasty, Severus Alexander had lost a war with the newly rising Sassanids leading to a renewed bout of fear towards the kind of oriental religion that Jupiter Dolichenus was kind of loosely inspired by. Plus Max was short on cash on account of doubling the army's pay in order to try buy their loyalty so he was looking for suitable targets to rob. So he went about destroying and looting the cult's temples.