All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the groom and his family believe that the dead have control over the universe, know the unseen, remove distresses (from people) and the like of what is exclusively related to Allaah The Almighty only, or they direct an act of worship such as supplication, slaughtering and the like to the dead people, then this is all included in the major form of Shirk that takes one out of the fold of Islam and it is not permissible to give your daughter in marriage to the one who holds that belief and does such polytheistic matters. For more benefit, please refer to Fataawa 82393 and 85126.
Accordingly, it is not permissible to let fear of shame prevent you from canceling that engagement. This has nothing to do with exaggeration or stupidity. Rather, this is something Islamically obligatory upon you. It is not important to know the name of the sect that they belong to; rather, what is important is to know the reality of their beliefs and acts because they are the main principles on which the ruling of marrying them is based.
As for your statement "we are Sunni Muslims and only believe in our beloved Prophet Muhammad, sallallaahu ‘alayhi wa sallam", we do not know what you mean by that. Sunni Muslims believe that Muhammad, sallallaahu ‘alayhi wa sallam, is the slave and messenger of Allaah and do not believe that the Prophet, sallallaahu ‘alayhi wa sallam, has something from the characteristics of Allaah, as Allaah The Almighty says (what means):
• {Say, "I hold not for myself [the power of] benefit or harm, except what Allaah has willed. And if I knew the unseen, I could have acquired much wealth, and no harm would have touched me. I am not except a warner and a bringer of good tidings to a people who believe."}[Quran 7:188]
• {Say, "I am only a man like you, to whom has been revealed that your god is one God. So whoever would hope for the meeting with his Lord - let him do righteous work and not associate in the worship of his Lord anyone."}[Quran 18:110], among many more other evidences.
Allaah Knows best.