An idealistic priest is hunted by Church agents after he uncovers a plot to release a virus that targets non believers.

Now *THAT*'s interesting.

Consider the word "Idealistic". To me, this sounds like a normal attribute of a priest rather than a fatal flaw.
I'd swap it for something describing a stronger flaw, or a deeper or ironic flaw.

Thanks to both of you for the feedback, I'll be back with a revision soon.

Originally it was intended as a discussion between religion and morality, the latter being being built on the former, but one being bent to an organisation's vision and the other interpreted on a personal level. If a devout priest discovered this plot by his own church, would his duty allow it to progress or would his (religion informed) morality force him to act against his church?
I take on board what you say regarding 'uncovers' and 'discovers', and to make it more a race against time I would have him discover the plot and then immediately being forced on the run.

The anti-virus is administered via Communion. Some people would naturally be immune and, if not devout, be hunted down and killed to allow no accidental access to a serum.

In a world increasingly pitted by the polarity between religion and atheism, I think the story gets its fair chance at the screens.

That said, you might want to determine in earnest where to stand between "uncovers" and discovers".

The former could take after the priest unassumingly having to mention it in an ethics column he handles in a provincial Christian newspaper; then the church authorities find out about that particular column edition.

The latter could take after church agents deciding to go after the priest after he naively mentioned it to a stranger ex-FBI operative he wasn't aware of in a monitored phone conversation, before now his fingerprints having been found on the locker of the digital safe where research documents on the virus are kept.

It's easily any writer's cut. Good one. Go for it.