I go monument -> shrine in my 2nd and third cities, and I think this is where craftsmen can trip you up a bit. With that solid monument bonus, you clearly want an early monument. But even with this amazing start, Craftsmen is very faith lite. Even going shrine first in my 4th and 5th cities (and with 1 quarry in my 5th city)....I founded on Turn 101. On an Immortal Start, that is on the razor's edge of not founding (I consider turn 100 a viable founder on Immortal, otherwise, your just gambling).
Now on the one hand, maybe craftsmen is better positioned for a Tradition play, and with that extra +3 faith it would make a big difference. On the other, the science from progress gets me the techs I need to start the Maus sooner, the extra worker, helps get the quarries going...and of course the +3 food helps compensate for the food lite quarries. So while tradition might help you found easier, I think progress has better synergy with this start. Ultimately I probably should have gone shrine first in my 2nd city to be more comfortable. Granted, that culture has been a godsend to get me in line for good wonders, but I think if I had done that, I could have likely gone monument 1st in the 3rd and 4th cities and still had a more comfortable faith position with a decent culture output.
But I did manage to found, and now I have a beastly production capital. Another side benefit of this opener is the availability of Stone works in my satellite cities. I am able to put 2 hammer ITRS to my capital. So now I've got a bonus +19 hammers, 14 from ITRs, and 5 from craftsmen. That's a +73% hammer boost from my capitals base production....huge!!! I am building the hanging gardens in 6 turns.
So overall, with this amazing start, I was able to make craftsmen work very well. The notes:
1) Craftsmen's niche is a quarry heavy opener where a Maus rush looks viable.
2) The monument bonus on craftsmen is anti-synergistic to your gameplan. You normally need to consider some shrine firsts in satellite cities...but the monument bonus makes you want to go monument first.
3) If you are able to found and have good quarries, craftsmen can provide a good amount of production and gold, which makes wonder production highly viable.
4) This has strong synergy with early hammer ITRs that can ramp up production in your capital.