Is it obligatory to completely refrain from shaking hands with foreign men, even if they extend their hands, especially if they are elderly, knowing that shaking hands is forbidden?

The ruling on shaking hands between non-mahram men and women has been previously explained in Fatwas numbered: 2248, 30543, 44821, and 31548. A Muslim should always be mindful of the greatness and majesty of Allah, feel shame before Him, and fear Him, rather than feeling shame before people. There is no obedience to a creature in disobedience to the Creator.