It's not an imbalance in the sense that it in-principal favors the AI over the player or the player over the AI. However it IS an imbalance (like many things in Civ, though that doesn't mean we shouldn't address them generally) in that it applies strong positive feedback to the leading player's power.
In general good game design applies negative feedback to power differences in an effort to keep things in check. The issue with GPs with DP, or indeed Wonders with techs, is that the leading player has better chances and that leads to a greater lead, and it snowballs. Thus it is that there is a tendency for someone to found far more religions than anyone else, or build far more wonders than anyone else, simply because they have what amounts to am increasing first-mover advantage.
So, the imbalance is in favour of the better (or if that's close, luckier start position) player, whether that be the AI or a human player.
Ok, I do agree with this. But that's a second modification to come to address all that. For now, its not as if the game has not classically supported, as you indicated, the problem with a snowballing lead in many more ways than simply Choose Religions or DP. And I wouldn't chastise or diss anyone who chose to play with either one off for just those reasons. Nevertheless, I like how both options spice things up a bit and allow for more choice and wouldn't want to see either one go as optional ways to play.
I've been giving some consideration to how the missionary option could harmonize with DP if both were selected... could be workable but I'd not mess with it until I had the other aforementioned solutions developed first to see if we still felt it was necessary.
Except that the AI prioritizes flavour religions over the endgame powerful ones. Is there any AI leader that would actually pick scientology first?
Well, I don't think any AI leaderheads consider it their favorite religion, so probably not, but past the favorite being taken, any leader that considers wealth a priority (and there's lots of those) would see Scientology as a very highly evaluated choice and would shoot for it immediately.
Before I got the 'Favorite selection first' portion working in the ai code, Scientology was sniped pretty quickly because I attempted to give some of the overall 'power' of the religion some consideration in the values I placed on their 'flavors'. It could certainly use a bit of auditing as I was assigning them off the top of my head without a full evaluation of each religion, but it seemed pretty fair at the time and seems to hold up still. I usually have to go for Asatru quickly because aggressives will flock to it immediately.
But the techs give you free great prophets, and without choose religion you can't found the religion without the techs, so it's essentially still the tech giving you the religion, just with the additional option of choosing where/if you want to found it. Which is the type of decision the player tends to be better at than the AI.
While SOME few religions could use being founded in cities other than your capital, I, as a player, usually want them all in my capital regardless, which is how the AI goes about it as well. I guess with that point I was just trying to make it more apparent that it takes a powerful persona to establish a religion rather than just the discovery of a new way to think.
Ok, so I do get what you're saying about the deity lvl play. We have issues with the ai keeping up in general and if that were to be identified and resolved (which we're always working on) we wouldn't have quite the ability to have a runaway monopoly on religions as you are showing. On Vanilla deity there's no hope of ever getting to a tech first and we realize this mod suffers some issues with the true difficulties matching the challenge degrees of the original. Some changes in the tech tree could be pending to assist that problem with Religious monopolies as well.