The Military Service Act of 1916 did contain a clause that allowed men to not serve on the grounds of conscience. Around 16,000 men called exemption on the grounds of conscience and appeared before a tribunal (type of court) to deem if their claims were true. Many COs were not given fair hearings at the tribunals:

Local authorities selected judging panels
Judges were normally too old to serve and believed people should dutifully fight for their country
Only 400 COs received exemption on the grounds of conscience

Absolutists were imprisoned for refusing to fight and many put in solitary confinement. Some COs faced extreme punishment of being sent to the frontline and given orders by the military there. If they refused to serve they would stand trial before a military court. Very few COs were executed, as the Prime Minister intervened to stop this punishment.