The Time Patrol opposes the Neldorians not because they commit murder but because they change the past. They would equally be time criminals if they saved lives - if that changed the past.
The Nantucketers oppose Walker because he is a threat and because:
"'When he spreads death, suffering, slavery, among the peoples here in our exile home, we bear part of the responsibility.'" (Against The Tide Of Years, p. 99)
They cannot object to Walker changing the past because they are already doing that merely by existing then. The only way not to change anything would have been to commit mass suicide immediately on arrival in 1250 BC - and there was one sect mad enough to try to kill everyone. Also, they realize that they are not preventing their remembered twentieth century from existing but are initiating a divergent timeline which hopefully will be better than the one from which they came.