I'm finding the Celts to be an interesting if not odd civ to play. I can't quite tell if I just don't have them figured out or they're on the under powered side of the spectrum.
First, their religion game is somewhat odd. They don't feel foreign passive pressure in owned cities if their city has their majority religion which is nice in the current patch where having to use inquisitors would be more harshly punished. However, they also don't push their own religion's pressure to foreign cities which makes spreading your religion really difficult- even if you invest in missionaries and spread to a non-founding AI it is difficult to maintain your religion in their cities without that base of passive pressure helping you. If you CAN push your religion onto them then they lose their pantheon (and can't use yours) so it can be a nice weapon to weaken your neighbors if you pull it off.
Because of the above mechanic, my strategy in most games has been to just get my religion spread to my own cities and then go for enhancement ASAP. I also purposely avoid founders like Council of Elders or Apostolic Tradition where active spreading is rewarded. Instead I've gone for the insular founders like Divine Inheritance or Theocratic Rule where you just get bonuses from golden ages or WLTKD regardless of your ability to spread. For follower beliefs I avoid buildings (the +passive pressure is largely useless on them) and just get yields from followers- your cities are typically near 100% following your religion anyway so it seems like the best choice.
Without a need to buy missionaries or religious buildings you end up with a bit of a glut of faith prior to the industrial era. Enhancing into Zealotry can provide a nice faith sink and save you a lot of hammers during that period, especially if you're being aggressive. You could also go for a Holy Site strategy and burn faith on prophets during this period.
The biggest drawback I see with their religion game is the difficulty in Reforming. Lacking passive pressure makes spreading difficult even to a non-founding civ if that civ has another AI that founded and is trying to spread to them. I've found that even if you convert a neighbor's cities another AI will come along and convert them to their religion and will win that battle against you due to having passive pressure as well. Conquering your way to a reformation is doable but the Celts really aren't THAT great at warmongering. Typically, even if you have high population or settle a lot of cities you can't meet the reformation threshold even with St. Basil so you're in a pretty tough spot.
Most notable in their religion are their unique pantheons I suppose. I think this part of their kit is what is supposed to carry them so making a good choice here seems very important. The Celts seem to be capable of pretty equally going Tradition/Progress/Authority in large part with pantheon choice and depending on your terrain. The science from jungle/forests from Cernunnos given a heavy forest/jungle start seems particularly strong for progress, for instance. Most of the pantheons are stronger versions of ones recognizable from the normal pantheon list so they act as a nice early game boost.
Next- the UU. The Pictish warrior is pretty straightforward, I think. You can get your pantheon from just 3 barbarian kills. If you go Mining as your first tech and upgrade your starting warrior to a Pict as soon as it finishes you can typically grab your pantheon sooner than if you went shrine first. My opening build order has typically been monument -> Picts x 3 to both tribute and barbarian hunt. The movement promotion for the Pict is also nice in terms of mobility to hunt barbarians and if the fights happen in favorable terrain they can cut through units fast. The faith on kill promotion doesn't stay on upgrade, unfortunately, but the main use of it is to get you your pantheon early and help ensure you get a religion.
Last- the Ceilidh Hall as the UB. The yields are pretty strong (especially with the bonuses from the pantheons) so it seems worth it to reach for this tech early and get them built ASAP. The musician specialist slot is nice for culture and can get you a few musicians earlier than normal (especially as Authority or Progress). Once you get musician guilds built, though, the extra slot from Ceilidh is contributing a much smaller percentage of your total musician GPPs and becomes less consequential as a result.
Overall, the Celts feel very 'jack of all trades, master of none' to me. They can seemingly pursue any play style given the right starting area but they probably don't do it quite as well as other civs who are more tailored to it specifically. I've mostly gone for aggressive Authority starts with them but warfare is probably more difficult and less rewarding as the Celts than many other civs. Being pretty good but not great at strategies is more likely to keep you viable throughout the game but less likely to actually win down the stretch.
First, their religion game is somewhat odd. They don't feel foreign passive pressure in owned cities if their city has their majority religion which is nice in the current patch where having to use inquisitors would be more harshly punished. However, they also don't push their own religion's pressure to foreign cities which makes spreading your religion really difficult- even if you invest in missionaries and spread to a non-founding AI it is difficult to maintain your religion in their cities without that base of passive pressure helping you. If you CAN push your religion onto them then they lose their pantheon (and can't use yours) so it can be a nice weapon to weaken your neighbors if you pull it off.
Because of the above mechanic, my strategy in most games has been to just get my religion spread to my own cities and then go for enhancement ASAP. I also purposely avoid founders like Council of Elders or Apostolic Tradition where active spreading is rewarded. Instead I've gone for the insular founders like Divine Inheritance or Theocratic Rule where you just get bonuses from golden ages or WLTKD regardless of your ability to spread. For follower beliefs I avoid buildings (the +passive pressure is largely useless on them) and just get yields from followers- your cities are typically near 100% following your religion anyway so it seems like the best choice.
Without a need to buy missionaries or religious buildings you end up with a bit of a glut of faith prior to the industrial era. Enhancing into Zealotry can provide a nice faith sink and save you a lot of hammers during that period, especially if you're being aggressive. You could also go for a Holy Site strategy and burn faith on prophets during this period.
The biggest drawback I see with their religion game is the difficulty in Reforming. Lacking passive pressure makes spreading difficult even to a non-founding civ if that civ has another AI that founded and is trying to spread to them. I've found that even if you convert a neighbor's cities another AI will come along and convert them to their religion and will win that battle against you due to having passive pressure as well. Conquering your way to a reformation is doable but the Celts really aren't THAT great at warmongering. Typically, even if you have high population or settle a lot of cities you can't meet the reformation threshold even with St. Basil so you're in a pretty tough spot.
Most notable in their religion are their unique pantheons I suppose. I think this part of their kit is what is supposed to carry them so making a good choice here seems very important. The Celts seem to be capable of pretty equally going Tradition/Progress/Authority in large part with pantheon choice and depending on your terrain. The science from jungle/forests from Cernunnos given a heavy forest/jungle start seems particularly strong for progress, for instance. Most of the pantheons are stronger versions of ones recognizable from the normal pantheon list so they act as a nice early game boost.
Next- the UU. The Pictish warrior is pretty straightforward, I think. You can get your pantheon from just 3 barbarian kills. If you go Mining as your first tech and upgrade your starting warrior to a Pict as soon as it finishes you can typically grab your pantheon sooner than if you went shrine first. My opening build order has typically been monument -> Picts x 3 to both tribute and barbarian hunt. The movement promotion for the Pict is also nice in terms of mobility to hunt barbarians and if the fights happen in favorable terrain they can cut through units fast. The faith on kill promotion doesn't stay on upgrade, unfortunately, but the main use of it is to get you your pantheon early and help ensure you get a religion.
Last- the Ceilidh Hall as the UB. The yields are pretty strong (especially with the bonuses from the pantheons) so it seems worth it to reach for this tech early and get them built ASAP. The musician specialist slot is nice for culture and can get you a few musicians earlier than normal (especially as Authority or Progress). Once you get musician guilds built, though, the extra slot from Ceilidh is contributing a much smaller percentage of your total musician GPPs and becomes less consequential as a result.
Overall, the Celts feel very 'jack of all trades, master of none' to me. They can seemingly pursue any play style given the right starting area but they probably don't do it quite as well as other civs who are more tailored to it specifically. I've mostly gone for aggressive Authority starts with them but warfare is probably more difficult and less rewarding as the Celts than many other civs. Being pretty good but not great at strategies is more likely to keep you viable throughout the game but less likely to actually win down the stretch.