He is talking about Ahlul-Bayt when the Shia don't recognize Aisha (ra) to be part of the prophet's (peace and blessings of Allah be upon him) household.
What about the Shia reviling Hafsa Omar - the other wife of the Prophet (peace and blessings of Allah be upon him)? Isn't she part of the Prophet's household?
Shia claiming Abubakar Sadiq (ra) is not a successor to the Prophet (peace and blessings of Allah be upon him) is the biggest hogwash that is ever told by any Muslim. Truth is, Abubakar Sadiq (ra) received the consensus of the entire of Umma at that time, and Ali Binu Abii Taalib (ra) reconciled with Abubakar Sadiq (ra), and accepted the leadership of Abubakar Sadiq (ra). Ali (ra) has even named some of his sons after the 3 first khalifs: Abubakar, Omar, and Uthman. So the question is if Ali (ra) named 3 of his sons after the 1st 3 khalifs, how is that Shia today reject the leadership of Umma by Abubakar (ra), Omar (ra), and Uthman (ra)? And if Ali (ra) accepted the leadership of Abubakar Sadiq (ra), how can Shia today make the claim that Abubakar Sadiq (ra) was not a successor?
If one belongs to Zaydi Shia, they are regarded as our fellow Muslims; however, Sunni Muslims should keep their distance from the Twelver Shia. Don't call them kuffars but keep your distance since they attribute their religious leaders with divine attributes.