No, it is not necessary to take drinks at a party. I assume you are referring to the alcoholic kind. Nobody should be obliged to consume an alcoholic drink merely because it is served at the party or because most of the guests are having them. Generally, guests at a party are known people and a thoughtful host will likely arrange to have non-alcoholic beverages served as well.
I do not think that drinking is considered as such to be modern or fashionable. It is simply part of a way of life at parties or other celebratory events of some people, much the same way as it may be considered the norm to serve only tea or coffee or other kinds of beverages by other people at their parties. For example, my friends may have a fine wine served at a birthday party in their home while I will serve juices and soft drinks at any get-together hosted by me. People don't need to justify their lifestyle to others or bother about others being judgemental. Let everyone party & celebrate the way they want to.
When people come at you with their worst, you should come at them with your best (advice given to Selena Gomez by her mother, quoted in Time magazine.)