Under US law the moment a person joins a religious organization they are subject to governing aspects of that organization, meaning that organization has a legal right to act toward the subject according to its dictates that are not illegal.
Under Watchtower's scheme the threshold “moment” is baptism.
This public marking is perfectly lawful under current US law, and a person subjects themselves to it legally at the point of baptism.
I'm sorry, but I'm going to have to continue to disagree with this because it is not accurate. I'm not trying to be argumentative and it's certainly nothing personal; rather I just don't want readers to have incorrect information.
This part of the above comment is completely circular: " a legal right to act toward the subject according to its dictates that are not illegal."
Any person in the world has a legal right to do things that aren't illegal. That's just the differece between legal and illegal. Baptism in and of itself does not give the Watchtower organization or any congregation any legal rights that it would not otherwise have toward a person. As I said, it might be one factor in determining whether you might welcome some of the normal things that church leaders do vis-a-vis their church members.
I previously asked for the specific U.S. law that you were referring to, and you cited a 12 page Watchtower legal letter that cited some cases. I did read the letter and I have previously read almost all of the cases cited in that letter, and none of them supports the assertion that you are making.
Edited to add: I will note that there is an 1871 Supreme Court case (Watson v. Jones) that does have language to the effect that you agree to follow the rules when you join an organization. However, this is misleading to have been quoted in a letter about baptism. That case was not about an individual member, it was about an individual congregation that wanted to leave the national church organization and keep their church building. The case was really not about an individual being subject to church rules, but a congregation being subject to church rules. This is a different matter, and there are legal rights that are affected when a congregation joins a larger church organization. The Watson language has never been used to apply to individuals being legally bound in secular law by church rules when they join.