Praise be to Allah.
The Standing Committee was asked the following question:
We come from a tribe that lives on the northern borders [of Saudi Arabia], and we mix with tribes from Iraq who are idolatrous Shi’ah; they worship domes and call them al-Hasan and al-Husayn and ‘Ali. When one of them stands up he says. “O ‘Ali, O Husayn.” Some people from our tribe have intermarried with them and mix with them in all circumstances. We have tried to teach them but they do not listen. I do not have enough knowledge to teach them but I hate what they do, and I do not mix with them. I have heard that we cannot eat meat slaughtered by them, but these people eat their meat and do not care. We are asking you what are our obligations in this case?
Answer:and blessings and peace be upon His Messenger and his family and companions.
If the situation is as you describe – that they call upon ‘Ali, al-Hasan and al-Husayn, and so on – then they are mushrikeen who are guilty of major shirk, which puts them beyond the pale of Islam. It is not permissible for Muslim women to marry them, and it is not permissible for us to marry their women, or to eat meat slaughtered by them.
Allaah says (interpretation of the meaning):
“And do not marry Al-Mushrikaat (idolatresses) till they believe (worship Allaah Alone). And indeed a slave woman who believes is better than a (free) Mushrikah (idolatress), even though she pleases you. And give not (your daughters) in marriage to Al-Mushrikoon till they believe (in Allaah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater), even though he pleases you. Those (Al-Mushrikoon) invite you to the Fire, but Allaah invites (you) to Paradise and forgiveness by His Leave, and makes His Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to mankind that they may remember”
And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and his family and companions.
From Fataawa al-Lajnah al-Daa’imah, 2/264
You have to advise your uncle and cousin, and tell them about the fatwas of the scholars concerning this issue. If your uncle insists on marrying his daughter to a Shi’i, then refer the matter to the sharee’ah court to prevent this evil action.
And Allaah knows best.
See also question no. 4569.