You have to do Hajj even if you go with the Shi’ah, if you are able to do Hajj. At the same time you have to beware of the specious arguments of the Shi’ah and their false way. If you can advise them and call them to embrace the way of Ahl al-Sunnah, then you have to do that, because Allaah says (interpretation of the meaning):
“Invite (mankind, O Muhammad) to the way of your Lord (i.e. Islam) with wisdom (i.e. with the Divine Revelation and the Qur’aan) and fair preaching, and argue with them in a way that is better”
And there are other verses which indicate that it is obligatory to call people to Allaah, and to enjoin what is good and forbid what is evil. May Allaah set all our affairs straight.
See al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta’, 11/18.