I'm going to go ahead and call you out on this one. The yields from Stars and Sky are far superior to the ones from Spirit of the desert. Food and Production are in my experience pretty evenly matched early on with production definitely taking the lead later on. Sure, growing your cities is nice, but you know what's also nice? Not falling behind on infrastructure. Getting Culture over Gold however is such a massive advantage that the entire discussion of food/production doesn't even matter. I personally really like the idea of early-game gold, it can translate into pretty much anything, but policy acquisition tends to snowball quite a bit so getting a cultural headstart on it is priceless.There is one big difference between these two pantheons. Spirit of the Desert gives you food, God of the Stars and Sky doesn't. We all know that lack of food is a major issue on tundra and desert (although flood plains can help counter this), so the +2 food on every improved resource is extremely powerful on Spirit of the Desert and it's harder to make Stars and Sky work, as it will be hard to to grow your cities and work many improved tiles. In addition to that, I feel that there are more resource tiles on desert than there are on tundra and a flood plains start in itself can easily be stronger than a grassland/plains/forest start, while a tundra start is almost alwaysa rerollbad. While both are too strong from my point of view, Spirit of the Desert is much stronger.
When it comes desert versus tundra I'm a bit more split, sure desert have floodplains, but floodplains doesn't really spawn that many resources outside of wheat. Most of your resources are probably going to land either in flat desert or in desert hills, making them a lot less workable than you'd like.
Tundra on the other hand pretty much only ever spawns resources in the forest, deer and fur, those tiles are really food-heavy either way so you're really not really starving yourself to work them.
If you have enough forest to auto-connect with iroquois you're probably better off picking goddess of renewal, especially since it also buffs your UB, which you're probably rushing either way.God of Commerce is great. If I play Carthage or the Iroquois, I always pick this. +4 gold and faith from the start is great. I'd say this is borderline overpowered but since it doesn't give you any culture, I'm not so sure about that and there sure are pantheons that are stronger than Commerce. Just look at Spirit of the Desert (that isn't even as strong as Festivals), which gives you the same +2 faith and gold on each improved desert resource but in addition to that, you'll get +2 food too.
The +1 faith for every 20 gold per turn you make doesn't make a big difference, the main point about this pantheon is the faith and gold you get from city connections. When you actually start to get lots of gold per turn, the value of faith has significantly decreased.