what is a word for someone highly invested in their religion?

Zealot?

Fanatic.

Faithful? Maybe.

What is a word for someone highly invested in their religion?

~~~ 'Brown nose'?
'Belief infested'?
'Listing' to one side!
Pathological?!

Lunatic.

Devout.

I think when you say invested, people tend to think negatively these days, but I would just say religious, spiritual, devout, committed, a missionary, possibly a witness, teacher, evangelist, rabbi, preacher, or advocate, fanatic, student or historian.