First, Ethiopia is almost certainly going to have a hill bias, so their maps will look similar to Greece's. 6-10 hills is more typical with Greece, at least for your core cities.I think people underestimate the sacrifice of forgoing mines on most of your hills. Using the rough-hewn church will basically cut your production in half across your empire, and if you don't save forests/rainforests until you can make lumber mills on them - which really happens too late to suffice, and you'd have to forgo chops - production might be so low that your cities aren't really functional at all. You really need a certain benchmark of production in order to play the game.
What few mines you might get from the church's adjacency restriction will not be enough. Keep in mind that you also pretty much have to settle on a hill, so that's another mine gone already. This will cripple nearly any city barring those with wildly improbable terrain, like 15 hills or a natural wonder that improves production surrounded by woods. Your typical city will have, what, maybe four hills? If you give up three of those for churches, that city will be stuck at like 12 production forever.
Second, who needs that much production for a culture victory? Each city only really needs to build a theater square. Everything after that is either supplementary or can be bought with faith and/or gold. 12 production per turn is fine for most cities, after a couple Magnus chops to get the theater square. Not saying that production is useless, but 1 production is worth about 2 faith, and I expect to build the rock hewn churches accordingly.
Finally, I think Ethiopia will have great synergy with earth goddess and work ethic. Earth goddess will further incentivize you to not build mines and work ethic offsets some of the loss of production.