Were they disrespected for being cowards or did people not mind?
From which country?
In Canada, there was a lot of dissent for the war (from both British and French, which started its own controversy) and objectors were protected by the federal government as much as possible, but were largely mocked and attitudes like "if you're not willing to go to war, you should not even be a citizen" were prevalent. In the end, a good chunk of people were conscripted but by choice put into manufacturing, intelligence and other non-frontline duties; they were in the war but not in the war.