Is it permissible for me to shake hands with my mother's maternal uncle? May Allah reward you with goodness.

The mother's maternal uncle is considered a maternal uncle, and he is among the unmarriageable kin (mahram) whom one is permitted to shake hands with. The proof for this is Allah's Almighty saying when mentioning forbidden relations: ﴿and the daughters of the brother and the daughters of the sister﴾ [An-Nisa: 23]. This is a point of consensus among scholars.