I just played a game with Saladin. I had to quit ~90 turns in because the experience was unpleasant. It was probably partly because I didn't play optimally, so I'll have another go at some point, but Saladin feels weird. His kit seems like it should be coherent, unlike those of some civs I think are terribly designed. In practice, though, his kit might actually be worse than just having no synergy like French Eleanor's because his abilities cannabalize each other.
What do I mean by this? First of all, campuses and holy sites compete for placement, so it's hard to get a great campus/holy site combo in a city. If you want to maximize your chance of achieving this combo, you need to play on Highlands, which is what I did, but Highlands is notoriously difficult to scout efficiently, and without any ancient era bonus (e.g. unique unit), it's very difficult to attain a Classical golden age. Failing to achieve a golden age somewhat defeats the purpose of trying to get good adjacencies on both districts, because you can't make use of good faith generation for the majority of the next era. There's also the problem of lack of food on Highlands, so the obligation of building two districts in your early cities is a big burden.
On a non-Highlands map, unless you're very lucky, you have to choose between a great holy site and a great campus. Prioritizing holy sites in your early cities means you're not making use of the Last Prophet ability, and your Madrasas will not be great. Prioritizing campuses means you'll have a more limited selection of religious beliefs. Also, benefits of religion don't scale well as the game goes on, and you can't even found a religion without a shrine, so there's the risk of not getting much out of religion if you choose to commit to campuses early game.
Arabia also suffers from the same problem most other science-focused civs do, which is that the Deity AI has an unreasonable obsession with campuses, making it difficult for the player to recruit any early Great Scientist. This is particularly bad for Saladin because I'd say Hypatia, Hildegard and Al-Zahrawi are all potentially valuable recruits.
Anyway, here is how I think Arabia can be improved. Instead of the Madrasa, I think Arabia should get a half-priced unique campus. I think this is really the only reasonable way for the player to compete with Scientist-hungry Deity AI. Keeping in line with the theme of the Madrasa, the unique campus should yield faith equal to science output. (Maybe, for balancing, this should be contingent on the cities with the campuses following Arabian religion?) In addition, Arabia's prophet should have the ability to instantly build a holy site when founding a religion. This holy site (and only this one) should have the special ability of producing missionaries without a shrine and getting a worship building without getting a temple first. This lays out a clear and straightforward strategy with Arabia:
1) Rush campuses in early cities (+4 era score for the 1st, which makes Classical golden age more achievable)
2) When a prophet arrives, found a religion and get a free holy site
3) Choose a worship building as the second belief (Mosque synergizes well)
4) Immediately build one in the holy site for 90% discount, using the faith accumulated from campuses
5) Buy a couple missionaries to spread the religion to Arabian and foreign cities
This version of Arabia should:
1) Stay competitive with Deity AI in the early Great Scientist race
2) Not have to worry about cannabalism between campuses and holy sites because technically only one holy site is required
3) More easily achieve a Classical golden age, having a good way to spend the copious amount of faith generated from campuses.
4) Have an extra economic policy slot, freed up from not having to plug in both Natural Philosophy and Scripture.