I also think that the double-culture is a minor thing. And the scientists are nice but you don't need them asap. It's a a balancing act between CoL and Music imo, in any case, Philo bulb will wait a little bit.
For me, the advantage of being CRE is the fact that you can increase your tech rate a little bit in a very sensitive phase of the game where you want to rush for Aest/Lit/Music.... Depending on who else is on the map, this can turn into a race where every single turn counts. You can easily lose Music to Asoka, Pacal, Suleiman etc... So 2 or 3 very early libraries can do the trick. Also border pops will help here, you settle food first, than grab a gold/silver mine in the 2. ring that you start working at 2 pop. With another library here, it's very good research. It's all about increasing your tech rate as much as you can and it's only about the immediate benefit.
Music is just so good : A perfect trait bait for anything you have neglected so far, and the GA/ Cathedrals/ Sistine. But I would try to build Sistine first before giving it away
(....not to mention that CRE can also help to reach marble in otherwise impossible locations. Much better than to settle a useless tundra city on the marble....)
FIN will also help to increase tech rate, but it is land dependent and it has a very short time-frame before scientists come into play. I would prefer CRE to FIN.
Am I wrong or are running scientists and working cottages two contradictory movements? So how could Elizabeth help me here except in coastal cities? In my games, I run artists all the time and do not even go back to slavery (if diplo allows me not to have to defend myself). I don't see a big use in FIN. Because later, irrigated farms are better than cottages, no? Building wealth in all the peripheric cities assures my culture rate at stable 80-90% normally.
All in all, I would say two religions are more than enough. If you have less than 9 cities you can boost 2 of your legendary cities with 2 cathedrals each while the 3. city tries to keep the head above water with a mix from settled artists/ great buildings and all the other culture buildings.