It's the other way around, actually. Justinian has Christianity as his favored religion, and so he pulls hard to Theology to land it.
Civic weights for the AIs are more about whether they will switch out of them or not. Saladin for example is also a religious zealot with Theocracy as his favored Civic, but he doesn't beeline Theology nearly as hard as Justin or Izzy. He's pretty content to stick with one of the early 2-3 until he picks up Islam later, as Divine Right is usually the last of the religion techs researched in a game (this is due to Science civs prioritizing Philisophy so much).
In response to OP:
I play almost exclusively on Immortal (sometimes fuddle around on Deity but never play to completion) with low sea level, Tropical climate, and a 7th AI (this give more, higher quality land and thus can speed up early-mid for human/AI depending on Jungle proliferation, but definitely makes the AI more powerful late game as well as speeds up tech pace after the early game)
Worker techs (any food techs, mining, BW, possibly Pottery) done by T50-60
Writing by T60-70
Alpha acquired (trade or otherwise) T85-95 -- this is very much determined by the speed of the AI!
Currency T110-120. My personal goal is T112 so i can get onto other things like maybe Music artist (around T120-125 it goes to the AI on Immortal)
subtract maybe 5min 10max turns on each for Deity for a strong open
after this the game opening is largely over and you should be deciding already who you are going to attack and with what to proceed on to winning later.
Liberalism should shoot for no later than 1000AD. In reality, the AI rarely beats this benchmark on Immortal (it's around 750- 800AD instead on Deity), but exceptional things can always happen; I've had Cyrus on Immortal snipe Lib before my projected 580-600AD once.
Other stuff:
1st settler T35-40
2nd settler T45-50
6 cities minimum by T90-100, more if you can float it (FIN+early pottery, ORG trait, gold tiles) but then wait until Currency to continue REX to 10-12. Note that I play expand heavy and crash my economy pretty much every game, I am just used to handling it for the greater land grab as a tradeoff.
Mids T70-75
GLH T75-80 (weirdly the AI is much better at somehow sniping this so as early as you can is always better)
GLib anywhere from 400BC to 400AD on Immortal. Almost always very early on Deity. It's the latest significant wonder and the AI like it, but a lot of inconsistency about when they pick it up
other wonder benchmarks aren't meaningful, really except maybe for failgold. Lots of variance in how the AI techs and prioritizes them
Can continue Cuir attacks as late as 1400AD or so, longer if you are very big or the AI is behind. Should plan to transition to Cavs or stop war and plan for tanks at that point. Tanks+Spy revolts are unstoppable unless the AI already has a million gunships before you even start, in which case you have to bait them into a city to whittle them down with CR2/3 tank hits.
Cannon attacks can go almost inifintely as long as you have at least muskets (Cannons can!). I've done Cannon+Infantry against Mech Infantry before pretty successfully. I have no idea about attack dates as I don't usually plan for Cannons, I plan Cav or Tank later instead after an earlier Cuir hit on 1-3 AIs.