I live in the traditional country and don't like this system.
This is a problem many have faced, even in the early days of Christianity. If you desire to seek something different, everyone else thinks you are insulting what they do.
You may want to start by explaining that you feel led to something more (additional). You may want to seek out others who have a similar desire. It is possible to have special fellowship, study, and prayer that makes traditional organizational programs, events, and rituals seem empty.
Usually the problem comes when a person considers discontinuing the empty and meaningless activities that mean so much to others. People might be able to tolerate someone who does something extra. However, doing something else completely is an undeniable statement that you thing what you do is "better" than what they do.
A person who lives in a Muslim country faces this problem if they are drawn to be a Christian. A person who lives in a Catholic country can face pressure from his family to continue Catholic traditions. A person who lives in a secular country can face pressure from his family to not become a Christian at all.
If we are drawn to follow truth, we will find ourselves in opposition to those who value comfort and tradition. We can still be a Christian in the isolation of a jail cell. How much more precious is the time when we can have fellowship with others who seek the Lord as strongly as we do.
Families often put pressure on us to conform to what they expect and desire. Sometimes this is for our own good and sometimes it is because family members want to feel comfortable themselves.
The title of your post is "go out?" To answer this you might have to ask another question, "go out where?"
Many people leave one church only to find another church that is just as bad or worse than the one they left. I think the best thing a Christian can do is think less of "where" and more of "who". The modern world is structured to reduce the significance of relationships. Christianity is supposed to be defined in the ministry (through relationships) we have with each other.
The first step in "going out" is to locate another Christian and cultivate a relationship with him. For example, a two person Bible study or prayer time may provide the depth of Christian experience for which you thirst. You may see an older wiser Christian who clearly shows the light and love of Christ in his life. You might ask this person to help you know Jesus as well as he does.
You may not want to take one big step "out", rather a series of smaller steps that focus on relationships and are more easily understood by family and neighbors. If they see you grow in faith and become more like Jesus, they may also come to desire what you have found.
Most Christians never realize when they have accepted the poverty of the comfort of the familiar instead of the riches of the joy of drawing nearer their Lord. If you start your quest to draw nearer to Jesus through relationships, you may not provoke as much criticism from others as you anticipate.