The U.S. Selective Service gives out a classification of “1-O” to Conscientious Objectors who apply for an exemption, which exempts them from both combat and non-combat military service. This can be given for both religious (i.e. Amish, Seventh-day Adventist, etc who object to any military service) or non-religious (secular pacifists opposed to war). America recognized conscientious objectors from the Revolutionary War (it varied by State, for example in Pennsylvania they would pay a fee) and in the Civil War it would cost a conscientious objector a $300 fee to be exempt. During World War II, the Defense Department had conscientious objectors file a DSS 47 form with ten questions in order to obtain an exemption.
So, no, legitimate conscientious objectors were never jailed. And, honestly, Briskers, Satmars, and really most other Chareidim who conscientiously object to the very State of Israel are true conscientious objectors.