You wouldn't think that shaking hands would be objectionable. The former pastor of a church I attended in the '80s, however, almost always skipped the portion of Mass in which the priest says, "Let us offer each other the sign of peace." Traditionally, congregants turn to each other and shake hands at that point.
Only once do I remember the pastor relenting. I'm guessing it was out of respect for a visiting priest who was sitting in at Mass. Even then, however, he couldn't bring himself to read the sentence as written. Instead, he said, "If you'll vow to each other a sign of peace, please..."
That was his compromise. A vow was permissible, but not a handshake. I'm surprised he didn't say, "If you'll nod ever so slightly to each other a sign of peace, please..."
