If it is, as was said - "
an exact copy" .. that according to you "
won't make a difference to other people or the version of you that steps out".
If your memories/experiences all come with, what difference does it make?
Unless you and TheDreamMaster are saying the version is
not and exact copy, and
will make a difference to you and everyone?
But you are not saying that.
Hmmm I'm thinking you're putting too much emphasize on the word "exact", and not nearly enough thought on "copy/replica". It doesn't matter how accurate a replica is; it doesn't change the fact that it is not the original, which can be affected by things independently of the replica and vice versa.
Let's look at it this way:
You get into a teleporter to go from point A to point C. Point B is the teleportation process itself.
You turn the teleporter on. You've reached Point B. The teleporter analyzes you for replication and then breaks you down to the atomic level, killing you.
Across the galaxy, at point C, the teleporter uses information from its analysis and constructs a duplicate of you. It's essentially a clone.
The original, true you ceased to exist at point B. Your body was destroyed, and your consciousness died with it. Yes, a copy of you may have walked out at Point C, but it is just a clone, a glorified photocopy of what the teleporter analyzed at point B. The original, true you does not continue being simply because a copy was made before death.
Look at it another way: if I photocopy a page from a book and then draw all over the duplicate page, the drawings don't magically appear on original page. That's because even though they both have the exact same text, they are still totally separate entities. In a similar vein, the point C version of you is an entity that is totally separate from the original point A you. Your consciousness does not carry over to the replica because it dies; the real you will not exist not be connected or share the experiences of the duplicate you. The duplicate you is nothing more than an artificial version, an imposter if you will.
Sure none of this will matter to the duplicate since he will be alive thinking he's you, and your friends and family can probably legitimize the situation, but it most certainly should matter to YOU, because when you step into that teleporter, YOU will die. You will cease to think, see, feel, breathe, you will cease to exist, and an artificial version will take your place. The accuracy of that replica won't change that fact.