YM, I can see your point of view; I avoid becoming too familiar with my students outside of class.
But I'd like to offer a different perspective.
Once you leave the school and go to another studio, teaching another art, it isn't about you and your students anymore. It is about you and your instructor.
Outside of the dojang and at another dojang, you are just a student, and if you can maintain a professional relationship and appropriate boundaries with your students in your own dojang, then certainly, you should be able to do so with them as a fellow student in another studio.
Also, if your students see you conducting yourself as an excellent student, you are then able to do something for them that you cannot do as an instructor: model appropriate student behavior.
Daniel
But I'd like to offer a different perspective.
Once you leave the school and go to another studio, teaching another art, it isn't about you and your students anymore. It is about you and your instructor.
Outside of the dojang and at another dojang, you are just a student, and if you can maintain a professional relationship and appropriate boundaries with your students in your own dojang, then certainly, you should be able to do so with them as a fellow student in another studio.
Also, if your students see you conducting yourself as an excellent student, you are then able to do something for them that you cannot do as an instructor: model appropriate student behavior.
Daniel