If you can take a moment and step outside the situation, think about this.
You and your girlfriend are holding hands in a coffee shop. You are both adults, 21 years of age. The wife of one of the elders of your girlfriend's church sees you holding hands, and this is a thing to fear? What business is it of hers?
Do you see the control that they have over your girlfriend? Do you realize that your every action will be monitored and scrutinized by people like this elder's wife, for the rest of your life?
You've been dating three months. Please, have a long talk with your parents, and understand that they fear losing you! Read experiences of the people on this forum, whose families have been torn apart by the Jehovah's Witness cult. Your parents' fear is real. There is a reason they do not like this religion.
There is an old expression, "Marry in haste, repent at leisure".