conscientious (adj.)

1610s, of persons, "controlled by conscience, governed by the known rules of right and wrong;" of conduct, etc., "regulated by conscience," 1630s, from Middle French conscientieux (16c.; Modern French consciencieux), from Medieval Latin conscientiosus, from Latin conscientia "sense of right, moral sense" (see conscience). Related: Conscientiously; conscientiousness.

Conscientious objector is from 1896, in reference to those with religious scruples about mandatory vaccination. Military sense predominated from World War I.

After a chequered career full of startling episodes and reversals, the Vaccination Bill becomes virtually the Vaccination Act. In Parliament the hottest of the contest centred round the conscientious objector. [The Lancet, Aug. 13, 1898] 

Slang shortening conchy is attested from 1917.