I am sure the Priest was not speaking against couples\families holding hands, my daughter will even hold my hand sometimes. He was speaking against everyone holding hands in imitation of the style of the non-catholics.
It is better to rediscover our Catholic faith and not be so eager to imitate other religious groups as it has led to a massive amount of confusion and loss of our Catholic identity. I don’t think holding hands is really a big thing but clapping is something that is totally inappropriate and doesn’t belong in every Sunday Mass.
There are a few exceptions to clapping such as the ordination of Seminarians. Yet when we start to change the Mass to a sort of performance where everyone is applauded for their parts we misrepresent the Holy Faith as taught by Christ which should worship God, not man.
In our culture today it is common for us to want to seek prominence and get people to clap for us which is why people enjoy it so much. It is natural to us as it is part of our non-christian culture these days to clap and seek approval from each other.
Mass is about worshipping God and doing it as the Body of Christ, all too often we have changed the focus on how can we together enjoy each others company. The Priest is probably trying to bring a little bit of God back into the Mass and highlight the fact that we are there for God first and then we exhibit our love for each other in our lives.