Well, I think everybody is overlooking the fact that in order to unlock a superior tier tenet you need a fixed number of tenets ie 3 tier-1 tenets for 2nd tier-2 tenet & 4 tier-2 tenets for 2nd tier-3 tenets.
Accordingly, the main sequence of tenet acquisition is :
1 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3
It accounts for 21 772 800 possible paths to complete it all !
Subsequently, each tier-3 favors one VC as previously stated in previews. It suggests that when starting ideology anyone should have a prefered victory to go for and choose tenets with this in mind. The first tier-3 cannot be chosen until the 6th unlock ! any tenet beyond that may be superfluous, so it's really 18 900 possible paths optimized to 10 800 possibilities ruling out UH.
Each ideology has 3 tier-3 tenets, and each of those tier-3 tenets is specifically targeted at one victory condition, so you're unlikely to want to open 2 tier-3 tenets. Of course you can only open a tier-3 tenet with the 6th unlick, but if you are the first to that ideology you get 2 free unlocks, so you only really need 4.