"Buying Tanks, Artillery, and Public Schools with faith is weak? "
Yes. Because you can also buy GS or GP from the faith. And you dont have faith for more that 5 tanks or 5 public school in a game.
"Goddess of the Hunt+Fertility Rites"
Very situational - also, the full tradition tree provide more food.
The faith threshold for GP grows exponentially higher with every bought GP. The faith threshold for units only increases by era and will likely depend on the cost in faith, information that we at the moment do not have. Regardless of this, there will come a point wherein buying GP with faith becomes inefficient, and if you are in any position whatsoever to use Jesuit Education or Religious Fervor, you will likely have a steady faith supply, enough at least to act as an extra city in terms of unit production. I've had games wherein the faith production was enough that even in the Modern era, I could afford a Lancer every other turn. We also have to consider the difficulty of actually finishing SP trees now. They take longer to finish, unless of course you aim for a complete culture game.
As for Goddess of the Hunt and Fertility Rites, I also added Sword into Plowshares/Feed the World as possible sources of food and growth, especially for Byzantium, showing that a well-founded Religion can be better than Tradition. This is not to claim that Religion will constantly be better than Tradition in food bonuses; the SP was designed for horizontal growth. It was to show that, given the right circumstances, that Religion can overpower Tradition, and that Religion is powerful because it is flexible. Religion supplements everything, and can be any bonus you wish it to be. That is its strength. It also comes into play earlier than Tradition's bonus, and is another factor to include. +2 food on turn 75 is good, but +2 food on turn 50 is better.
Good question (is it 2 pantheons or 1 pantheon & 1 bonus)
I'm also wondering if it works with a Pantheon. ie if a pantheon is the second most common 'religion' will it still get its effect?
(That would make religious tolerance useful if you hadn't fouded a religion yet, and someone else's was invading your cities)
IIRC, Byzantium gets a Bonus Belief, and not necessarily another Pantheon. I think they would simply restrict Religious Tolerance to Byzantium's Pantheon and not their Bonus Belief, even if what is chosen is technically a Pantheon.
I frankly I don't know about that reformation belief. The piety tree also allow you to get any kind of great persons with faith and you need more than before because now there are three cultural great persons which you'd need even as a warmonger if you don't want to get heavy happiness issues.
The fact is that you can get units through money and through regular buildings, great persons however can't be acquired so easily. Faith is the only way you can buy them, but they cost a lot of faith.
Do you really want to waste precious faith in units and buildings that you can buy with money?
Depends, really. Buying GP with Faith comes with diminishing returns. To get the full use of Faith for GP requires excluding the option to buy post-Industrial land units and as such it is not really a fair comparison. You and I would both agree that we'd pick For the Glory of God and/or Jesuit Education if given the chance but Religion works on a first-come-first-served basis and we may not always have that luxury. Every other Reformation belief aside from those two, and arguably Religious Fervor, are situational at best and tailored to either the Diplomatic/Cultural victory. For Religious Fervor, we must first know how much each unit costs. If it is ridiculous, we skip it, otherwise Religious Fervor would likely be our go-to choice once FtGoG or JE are taken.
Edit: Okay, I've just checked the Screenshot Thread. Apparently, Comanche Cavalry costs about 300 Faith at what we can assume is Quick Speed. We can infer then that Cavalry costs about 340-350 base Faith on Quick Speed. Assuming they increase in costs with era, you would likely be better off spending on the early-Industrial units and late-game buying is probably infeasible. With these costs though, rush-buying Artillery is very feasible at only a slightly higher production mark-up in comparison to the Cavalry, about 400 Faith if my numbers are right. Make of that what you will.
does not hold up against the policies from Liberty and Honour. So while it is a worthwile strategy, there isn't much variation here.
