Answered by Shaykh Faraz Rabbani
I was doing dhikr on my fingers of both hands and one brother came upto me and told me not to do dhikr on left hand because prophet Muhammed peace be upon him said to do all good things with right hand. He also said that we clean ourselves with the left hand so its not proper to do dhikr with the same hand. Some time later another brother told me that its sunnah to do dhikr with both hands!
It is recommended to do all noble things with the right hand. If one does this, with an intention of following the noble way of the Messenger of Allah (blessings and peace be upon him, his family, and companions), one is rewarded. But one is not blamed for non-performance of such matters. [Imam al-Ayni, Umdat al-Qari Sharh Sahih al-Bukhari]
The same applies, Imam al-Ayni says, to eating with the left hand. The vast majority of the scholars, except the Literalists, held that it is recommended to eat with the right hand, but it is not something that is sinful or blameworthy if left out, unless one does so out of disregard or disrespect for the sunna of the Beloved of Allah (Allah bless him & give him peace).
Therefore, it is permitted to do dhikr with both hands. Some scholars preferred this, so that all one’s fingers would bear witness for one’s worship on the Day of Judgment. Others preferred that one limit oneself to the right hand, because, as `A’isha (Allah be pleased with him) mentioned, “The Messenger of Allah (blessings and peace be upon him, his family, and companions) like to use the right in all things.”
Thus, it is a difference of preference, not permissibility.