Yes.   If your plan will not initially cover the method your provider recommends, you should ask your provider to request a “waiver” or “exception” from your insurance plan. However, if you are enrolled in an employer plan, and the employer has a religious or moral objection to contraceptives, your plan might not include contraceptive coverage.

Short-term health insurance policies do not have to provide benefits required by the ACA, including contraceptive services.  Health care sharing ministries, which are membership groups usually affiliated with a religion that help members pay for health care (not insurance), are also not subject to ACA benefit requirements.