I suspect you are correct. My last game was better than my previous ones precisely because fewer religions spread and I was forced to build fewer cathedrals.
I´m going to try superhard in my next game to sit on my hands after 250AD i.e. let any cats finish themselves and not start any new ones and see where that gets me.
Try building every Cathedral you have the religion and strategic (hammer doubling) resource for. Never gold rush these.
If you are missing the strategic resource, think hard about building that Cathedral. These can be gold rushed into hammer poor cultural cities, but these are also the cities that should be bombed by late GAs. If you do build them, they should be the last Cathedrals you build, since they take forever to build; you want the cultural multiplying effect of your cheaper Cathedrals while building these expensive ones.
Don't be shy about gold rushing temples you need to allow the corresponding Cathedral, especial if you want to build that Cathedral in 1-2 turns. Hammer build the temples for at least 1 turn to avoid the 4.5 gold per hammer price. 3 gold per hammer is bad enough.
Non-Cathedral related ideas:
For normal speed, early GAs probably could be settled. It's hard to compute the turn at which GAs should be saved. I'd say, error on the side of saving GAs earlier than you think may be optimal, since it will be much easier to know where to bomb them on the last few turns than where to settle them early.
BTW, turn 120 for Liberalism may be a little too aggressive. I'd say that turn 125 (AD 250) is right on target.
Don't forgot to run the cultural slider as high as possible. The best way to use gold is to save it till later after all Cathedrals are build and use that gold (deficit spent) to run the cultural slider at 100% until you run of gold and win (ideally at the same time).
Build as few non-culture adding buildings as possible. About the only exception is the Aqueduct and maybe Grocer for adding Health when absolutely necessary. However, running a city at a large negative Health can be better than building these Health buildings, especially later in the game.
Sun Tzu Wu