Does shaking hands with other sexes invalidates one’s ablution?

The purity that ablution gives is a mental one, to allow a Muslim to offer prayers and do some other acts of worship. It is not physical purity that removes anything tangible. The Prophet, peace be upon him, was asked whether a believer gets impure, and he said that no believer, man or woman, becomes impure. If you have had your ablutions and needed to shake hands with a non-Muslim or with a Muslim who is not in the Purity State, your ablution remains valid and you can go ahead and offer your prayer in the normal way.