Allah (SWT) Has kept every Infallible totally pure, and kept any type of impurity far away from them, not that Allah has removed impurity from them, but kept them far away from any impurity i.e. Allah did not allow any impurity whatsoever to come near any Infallible. Quranic verse 33:33 stated: In fact, Allah wants to keep impurity away from you O, Ahlul Bayt إنما يريد الله ليذهب عنكم الرجس أهل البيت
There is a big difference between ليذهب عنكم to drive away any impurity from coming near you, and ليذهب منكم which means to drive away impurity from you which can mean driving away any existing impurity. Allah (SWT) never said that, but He said ليذهب عنكم which means that Ahlul Bayt never had any impurity, and Allah kept impurity far away from coming near them.
All the existence of the Infallible is absolute pure in the highest level which can never be compared with ordinary pious people.
These facts are very clear in Quran and the authentic Hadeeths. After believing in these facts, we do not need to go into details of the personal life of the Infallible, which are not necessary for us as it has nothing to do with our faith and practice and our responsibility to be sincere and humble servants of Allah and obedient followers of the Prophet (SWT) and Ahlul Bayt(AS).