Great question! Two key points to make to that...
First, by far the best way to get a sense of early build orders is to look at Succession Game 'regular' games. The early moves are scrutinized by most other players on the team and after playing many such games, most openings are quite solid.
Second, there is for me absolutely no set pattern for the opening build. It depends on so much - difficulty, game goal, variant conditions, and very much on the food and shield mix of the capital and early cities.
So let me share some key principles I keep in mind, then finish up with some 'common' build orders. If my capital is low food and high shield I will look to use it for the unit production of the nation and let early new citeis take up the task of settler and worker production. If there is a +5 food ~5spt city site that's the closest thing to dogmatism - I build a granary in it immediately and make a worker farm (or better, a settler farm). Depending on the situation it's either: granary - settler - warrior - settler ad infinitum or granary -worker - ad infinitum. No temples, no rax, no troops.
Second, if my capital is that +5 food high shield workhorse, I reverse things. My second city becomes a rax - spear - spear - spear machine. Capital stays on settlers until it has spit out probably a dozen. Third city will probably build workers or exploring units or a granary or a boat.
I seldom build early temples, unless: I'm religious... or I NEED a temple to pull in an important resource, or I'm going for a culture win. I tend to like granaries in a decent number of early cities - more when more rivers, almost none if I decide to get the Pyramids, less if high food but low shield.
Ironically, the higher the difficult the LESS troops I build, and tend to go with 2-3 warriors for exploration and that's IT until I have as many cities founded as the expansion-rabid AI will let me have peacefully, caving in to the assured tribute demands, then when land is gone very quickly getting some defenders everywhere and turning attention to the economy using cardboard cutout defense.
On a lower diff or where the game rules or situation dictate ancient war (e.g. I'm Iroquois next to Rome who is slow to Iron working or hooking up iron, or Germans next to the Indians, etc) - then and only then would I build more than a single rax. In that situation though, I tend to favor a four-city all rax plus offense unit (temple? no way) and start the war ASAP, capturing the capital and about 2 other cities plus about 2 techs for peace, then hit them again in 20 turns.
On an archipelago things are different yet again. I forget military almost completely and go for settlers and boats.
So above are described 3-4 situation-specific build sequences. In a typical potluck situation with a totally plain looking start, I would still tend to specialize my cities, and not use the same order in each. Perhaps a quick worker from each so that I didn't get "behind", followed possibly by a warrior for cheap exploration or MP, then a granary in one of the cities, a rax in another, and a boat or temple in a third. The granary city would follow up with workers/settlers, the rax city with spears at least one per city in the empire, then start adding some offense to the mix for barbarian control (opposite priority of offense and defnese if I'm going for a blitz early war)
Now, if you like the set order you mentioned because you can't stand even a chance of culture flips, and if you in almost every game like hitting the AI quickly, it may work fine for you. I would however suggest you consider the power of early granaries, the inefficiency of not having more specialization in cities, and definitely that you become more situational and dynamic in choosing early build queue orders.