All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If this woman sticks to and believes in deviated principles like accusing caliphs ‘Umar and Abu Bakr of defamation and even of disbelief, or saying that the Quran has undergone changes, or considering supplicating or offering vows to Awliya (pious people) and Imams as lawful, or believing that the Awliya and the offsprings of Al-Hassan and Al-Hussayn know the unseen and similar deviated matters; then if this woman believes in any of the above, it is unlawful for the Muslim to marry her.
But if this woman believes in some innovations that do not reach Kufr, or if she is attributed to some deviated groups only by name, then this man could marry her. But the Islamic center should teach him the right creed and warn him against the innovations and aberrations of the deviated groups especially that the man you mentioned is a new Muslim. You should tell him to express clearly and forthrightly his opposition to the innovations and aberrations cited above. If he notices any desistance from her side, or realizes that she is surrounded by relatives who believe firmly in the misleading ideas cited above and if he fears for himself or for his children, then he should not marry her. This man should then look for a pious Muslim woman who would raise his children on the love of the Quran, the Sunnah, and the Companion's of the Prophet who brought this great religion of Islam to us. In fact, all the good we enjoy now is but one of their good deeds. (i.e., they will be rewarded for it)
Allah knows best.