WASHINGTON — More than 12,000 military service members refusing the COVID-19 vaccine are seeking religious exemptions, and so far they are having zero success.

That total lack of approvals is creating new tensions within the military, even as the vast majority of the armed forces have gotten vaccinated.

The services, urgently trying to keep the coronavirus pandemic in check by getting troops vaccinated, are now besieged with exemption requests they are unlikely to approve. Meanwhile, troops claiming religious reasons for avoiding the shots are perplexed because exemptions are theoretically available, yet seem impossible to obtain.

Caught in the middle are chaplains, who must balance the desire to offer compassionate care and guidance to personnel with the need to explain a complicated process that may well be futile.

According to the services, at least 30,000 service members are not yet vaccinated, but several thousand of those have gotten temporary or permanent medical or administrative exemptions approved. Of the remaining — which is likely 20,000 or more — thousands are working their way through the exemptions process, such as for religious reasons, or have flatly refused. That’s about 1.5% of the roughly 1.3 million active duty troops.