What kind of movement or denomination in Christianity made being a Christian a personal/individual choice? What kind of movement or denomination in Christianity made being a Christian a personal/individual choice?

I recently watched a random YouTube video. Random, because I had no idea how I got there. The person was Jessica Kellgren-Fozard. Basically, she's born in a Quaker family. But she didn't say that. She said her mother was Quaker, and when she became 16, she made a choice to become Quaker. Her way of expressing essentially emphasized her individual choice. 

I am also aware that Baptists share the same mindset. Baptists may say that they are Christians, and they are raising children to become Christians, but the children have to make choice whether or not they want to become Christian. In other words, Christianity has become a personal/individual choice for Baptists.

Then, there are Catholics. In Roman Catholicism, there seems to be no way to become non-Catholic. A person is born into a Catholic family, baptized as a baby, raised Catholic and remains Catholic. That person may not attend church permanently, not tithe, not even believe in God, but that person is still Catholic. 

Is the emphasis on individual choice a Protestant characteristic?
The earliest reference I can find to individuals confessing their faith in Christ and asking to be baptised (as an adult believer) thereby making a  personal choice, dates back to the early 16th century when the Anabaptists rejected infant baptism and went about re-baptising  adults who had previously been baptised as infants:

The early Anabaptists formulated their beliefs in the Schleitheim Confession, in 1527. Anabaptists believe that baptism is valid only when the candidate confesses his or her faith in Christ and wants to be baptized. This believer's baptism is opposed to baptism of infants, who are not able to make a conscious decision to be baptized. Anabaptists are those who are in a traditional line with the early Anabaptists of the 16th century. Other Christian groups with different roots also practice believer's baptism, such as Baptists, but these groups are not seen as Anabaptist. The Amish, Hutterites, and Mennonites are direct descendants of the early Anabaptist movement. Schwarzenau Brethren, Bruderhof, and the Apostolic Christian Church are considered later developments among the Anabaptists.
The name Anabaptist means &quot;one who baptizes again&quot;. Their persecutors named them this, referring to the practice of baptizing persons when they converted or declared their faith in Christ, even if they had been baptized as infants. Anabaptists required that baptismal candidates be able to make a confession of faith that is freely chosen and so rejected baptism of infants. The early members of this movement did not accept the name Anabaptist, claiming that infant baptism was not part of scripture and was therefore null and void.  https://en.wikipedia.org/wiki/Anabaptism

I also found a reference to Martin Luther (taken from his Small Catechism) on the subject of the sacrament of holy baptism, which quotes Mark 16:16:

Christ, our Lord, says in the last chapter of Mark: He that believeth and is baptized shall be saved; but he that believeth not shall be damned.  https://en.wikisource.org/wiki/Luther%27s_Small_Catechism#IV._THE_SACRAMENT_OF_HOLY_BAPTISM

Although I could not find anything to suggest that Martin Luther denounced infant baptism and promoted the view that only believing and consenting adults should make a decision to come forward for baptism as a declaration of their faith in Christ Jesus, that does not mean to say such a quote does not exist.  The emphasis on individual choice is a distinct Protestant characteristic which came out of the Protestant Reformation.