Regardless of the existence of souls, or flying spaghetti monsters, or any other supernatural force - a transporter basically amounts to a 3D fax machine.
It scans an object, converts it into a digital, electrical signal composed of instructions on how to build "you", and the object gets printed on the receiving side. Sending blueprints of a human is a lot more probable than breaking apart your individual atoms, converting them all to energy, and then reconverting/rebuilding you the exact same atoms in the exact same locations.
Most likely you would be discarded and a new being with your memories and attributes would be created. If it were you, you'd simply be killed while another entity carried on your existence. To the outside world and to the most recent copy of you, this shedding of lives would cause no perceptible changes.