Burn the dead bodies. Not kill the living. Quit conflating shit.
...and this goes out to Trekker4747, too:
They were dying. Carol was the witness--Rick was not
. He did not know what he was talking about. Carol protected the group while Rick was playing farmer.
In Caleb's case, Hershel was able to see what happens for himself--and why Caleb rejected his attempt to help him. There is no help at that point and death/reanimation cannot be avoided.
Again, Karen and the other guy were already sick
, and were not going to improve as they were among the first to show symptoms (after the nerd), so the disease was well on its way to ending their lives. Any objective mind knows they were not going to survive the time Daryl's party was away.
So, what we have is Rick--based on his fantasy of Carol's action (notice he imagines Karen was sleeping--not hacking/succumbing--her real condition) makes a "Ricktatorship" decision--not a word with anyone else.
You must realize Carol will return to save his ass--or be the instrument for a new level of pain.
If it happens, I cannot say he did not ask for it.