Anyone who is unable to do military service for reasons of conscience can submit an application to be allowed to do civil service. The applicant is then invited to a hearing where he is asked to explain his reasons for refusal. After this hearing, the application is approved should the applicant be found to be unable to be a member of a military service due to the demands of his conscience; in most cases it is approved (currently in about 90%).
Once part of the civil service program, one has to work for 1.5 times longer the military service period refused; (full military service is currently 300 days). Many non-profit organizations are licensed to be able to employ civil service workers.
There are still issues with how to handle Swiss living abroad, as every step of the process requires their presence in Switzerland.