"Soul conceit" is the right term here. The belief humans can't seem to shake that I am more than just the sum of my parts.
I don't know if I have a soul or if my consciousness is really just electric meat. But it seems that if I am more than the sum of my parts, the soulless me that comes out the other side will just be "my parts" and will be obviously different than the original me.
If we really are just our atoms, and the technology can be trusted to reliably replicate me atom for atom on the other side then there's nothing to be afraid of. The original you hasn't died, it's just ceased to exist. No big deal. The clone of you is also you, so you still exist.
If you have no soul and you just exist as matter, then in a horrible transporter accident where your clone and your original still exist, now there are two of you. You are both you. There is no difference if you are both perfect copies of each other. 1=1.
Sounds like a win/win to me, finally a best friend who really gets me.