For the person about to step into teleporter, there's a true difference, even if it not observable from the outside.

Sure. For every person about to go to bed, there's also a true difference between the way they are as they go to bed, and the way they are as they wake up.

That there is a true difference doesn't really matter much; a more useful question is whether we value the difference... which is a psychological and social question. When you insist on ignoring social norms, the effect is simply to insist that a particular set of social norms (the ones having to do with continuous existence in a single body being important) be given unexamined primacy.

Which is fine for you, since you embrace that set. For those of us who reject it, it just seems like a goofy thing to insist on.