I'm just going to go ahead and reference the movie The 6th Day. Yes, it's a rather terrible movie, but shows the problem pretty clearly.
The only way I'd be on board with acting without fear of death due to cloning replacements being an option would be with the EVE Online model- that is, you have a ready-made clone for insurance purposes, with a brain implant version of a CD burner. While piloting your ship via hydrostatic pod, and I suppose since Dust 514, while implanted with pod-pilot style brain implants, the instant you're killed (or specifically while piloting a ship, the instant the pod is breached) a snap perfect brain-scan is made, which by the nature of the technology (though also intended) is destructive. An immediate transfer, while the scan is in progress, to your clone is made, creating neuropathways and activating synapses precisely as it was in the previous head, so precise and rapidly that not a beat is missed in the transfer of consciousness.
While this still sounds a bit unsettling, especially with regards to the "that's not really ME me" thing, taken with another bit of technology in game, which by lore is paired with the above mentioned technology, makes me feel a bit more at ease with it.
Infomorph Psychology:
"Psychological training that strengthens the pilot's mental tenacity. The reality of having one's consciousness detached from one's physical form, scattered across the galaxy and then placed in a vat-grown clone can be very unsettling to the untrained mind.
Allows 1 jump clone per level."
There's already another mechanic in-game who's lore specifically references transfer of consciousness. In game, in addition to your "insurance" clone, you can have multiple "jump clones" that you can position around places you'd need to get to quickly, or just need to transition to without making a huge trip out of it (have one out in nul-sec for pvp warfare, and have one back in empire space for commerce/'vacation'). The transfer in this case is non-destructive, and no cut/paste is going on, more of a syncing. Plus, as the whole thing was made to be very meta, since it is still YOU playing, then it's intended to imply a transfer of consciousness, not just a copy.