Religionist.
I would say Christian or believer.
Not all churches are Christian, and neither are all believers.
Believer would sound good. “Believer” is very broad and covers pretty much anyone with a religious belief. “Follower” can imply that the person is following an organized belief system, potentially one that is implied in the context of the description. Without a religious context, “follower” may not have the implication you want, as one can also be a “follower” of a political ideology, social trend/fashion/fad, or sport. “Parishioner” implies that the person participates in a specific congregation.
Thesaurus says (among others):
Or you could just call them all “Fido”. 
Have you read the thread? The whole thing started because the OP didn’t want to use a term that referred only to Christians.
The trouble with “believer” is that, because of common usage, most will assume you mean “Christian” only. People that describe themselves as “believers” are almost exclusively Christian, and most of them think that the word alone is enough to let people know what religion they belong to.
At this point, I will probably stay with “churchgoer” even though that will rankle a little with non-Christian readers. That says what I want to say, albeit with connotations I’d like to avoid. There’s time to change it - months, really - so further contributions are welcome.
If I haven’t made it completely clear, I am looking for a term that represents the individual as the member of a self-defined class that defines who they are in a social sense - e.g, you might choose from a long list “parent,” “professional,” “businessperson,” “engineer,” “homemaker,” and, if your religious practice is a defining aspect, whatever word I can’t find to replace “churchgoer.” It’s not meant to analyze the content or viewpoint, just the social component. Most of the alternatives presented get too far into the nature or depth of “belief” or practice.
“Congregant” is a little better but seems Christian-biased; do temples and mosques have “congregations”? Unitarians? Greek Orthodox?
Jewish synagogues are often Congregations. My previous synagogue was “Congregation Adath Israel”, or CAI for short.
Interesting question! I’m not sure if there would be a single word that would properly apply to all religions, but even so, seeing what words get closer/closest to the desired meaning is fun.
“Adherent” came to my mind, since it has, IMHO, the implication that the person is more likely to attend the services/ceremonies of their faith (compared to “believer” or “faithful”), but it’s not quite right either.
I found a related discussion on Wikipedia. It really only relates to Christian denominations, but it shows how “churchgoer” and possible synonyms aren’t all applicable even within Christianity.
“Adherent” means “supporter of cause or leader”-not necessarily religious.
Worshipper?
As this thread has shown, there really isn’t a single word that accurately conveys your intended meaning. Though it’s not as tidy as a single word, I think “person of faith” conveys it best, even better than “churchgoer.”
And it will rankle because it marginalizes them. As long as you’re OK with that I don’t see a problem. But “person of faith” is a better choice regardless.
Putting that phrase into Google brings up mostly Christian connotations.
I can understand why you find “person of faith” to be “lumpy and precious”; but also, it doesn’t really indicate what the person does or what role they play, the way “churchgoer” and the other words on your list do.
If it were my choice, I’d probably go with “religious person” or “member of a religious community.” That’s a bit clunky and unsatisfying, but I can’t think of a better term with the same generality.
What do I win?
He’s looking for a noun, like parent, professor, student etc. Devout is an adjective.
I still think “religionist” works best-it’s a word instead of a phrase, and it isn’t already used almost exclusively by any particular religion.
Ah. So, devout believer/Christian/Jew/Muslim/Baptist then? Or devotee then, but that has already been mentioned several times.