In the US, the draft board will want to see evidence that your views have influenced your life for a period of time before filing for CO status. But, yes, the criteria for granting CO status are hazy. Whether someone qualifies, or doesn’t qualify, is at the discretion of the draft board.
Here is a bit of information from the US Selective Service about CO status:
*WHO QUALIFIES?
Beliefs which qualify a registrant for CO status may be religious in nature, but don’t have to be. Beliefs may be moral or ethical; however, a man’s reasons for not wanting to participate in a war must not be based on politics, expediency, or self-interest. In general, the man’s lifestyle prior to making his claim must reflect his current claims.
SERVICE AS A CONSCIENTIOUS OBJECTOR
Two types of service are available to conscientious objectors, and the type assigned is determined by the individual’s specific beliefs. The person who is opposed to any form of military service will be assigned to Alternative Service - described below. The person whose beliefs allow him to serve in the military but in a noncombatant capacity will serve in the Armed Forces but will not be assigned training or duties that include using weapons.
ALTERNATIVE SERVICE
Conscientious Objectors opposed to serving in the military will be placed in the Selective Service Alternative Service Program. This program attempts to match COs with local employers. Many types of jobs are available, however the job must be deemed to make a meaningful contribution to the maintenance of the national health, safety, and interest. Examples of Alternative Service are jobs in:
Code:
conservation
caring for the very young or very old
education
health care
Length of service in the program will equal the amount of time a man would have served in the military, usually 24 months. *
sss.gov/FSconsobj.htm
(more information is at the link)
I am fairly certain that many men who served in the Vietnam War did not support it, but they served when drafted.