I'm not sure how Raging Barbs play out exactly. Extra safety can be a reason to max

in Delhi.
But growing to 6 is just that : maximizing hammers in Delhi.
If it delays the second city, then, overall, it's a loss. The city tile produces 2F1H1C at least and then there's a special that can be improved. Growing 1 more size on a blank forest doesn't compare very well (+1H per pop).
Consider this :
2pop whip = 60H
1 chop = 20H
2 turns building the settler at size 4 = 20+H (depends whether a mine is improved or not)
So at size 4, with a 2pop whip, the settler can be out on the 4th turn (2 turns investing hammers, 1 turn whipping).
Meanwhile, Delhi, from size 3, can produce a maximum of 8 Food per turn.
That's 11 turns to grow from size 3 to 6 and 8 turns to grow from size 4 to 6.
There's the delay
It may not be the best choice to 2pop whip at size 4, however. That loses the rice tile for 4 turns or so (= -8 food ; unless the rice is shared with the second city ... but if it is, then that city needs a Monument first... not too good.)
A 1pop whip is also a valid approach :
1pop whip is 30H
2 chops are 40H
3 turns are 30+H
--> settler out on the 5th turn ... Not sure the worker turns allow that. It would make it a lot easier to grow back to size 4 and start on another build (hence justifying the 1 turn delay on the 1st settler).
or :
1pop whip is 30H
1 chop is 20H
5 turns are 50H
--> settler out on the 7th turn. Still faster than growing 4->6 over 8 turns.
If one doesn't want to lose the yield from the rice (at the cost of delaying whatever special is settled first),
Then a 2pop whip at size 5 can also be considered. I'm quite sure it's better than a 3pop whip from size 6 as well