Hagia is a nice GB (Happiness and FP are both useful), it is cheap in goods, and BP's are easy to get.
As it has been pointed out though, the issue is that its efficiency (happiness per tile, compared to other buildings) goes down as you progress through the ages.
So you should build the Hagia IF: you build it early (EMA), level it fast, and plan to progress *slowly* through the ages. Then the Hagia will have time to more than repay your investment in it, and it will be an extremely useful GB.
You should not build it, if any of the above conditions is not true (ie if one is already in LMA, CA or later (already too late), plan to leave it at level 3, or plan to move relatively fast through the ages.Then the Hagia will not have enough time to be really useful (which is to take care of your people's happiness while you are at EMA through, say, IndA, plus give you some extra fp).
I have been playing for 15 months and I am still in CA (and not planning to progress further any time soon). I built it at EMA and got it to level 5, then for most of HMA it was at level 7-8, at LMA at level 9, and at CA at level 10. I also have a high-ish Dresden, and never needed to bother with cultural buildings (until my Habitat got to level 7, and then I built one cultural building). To me the Hagia is worth its weight in gold. But that is because I stayed long in each age, levelling my GB's (including Hagia). You do not need to go as slow as me for the Hagia to be useful; but if you plan to move relatively quickly through the ages, then do not build it, because it will not have a chance to be very useful for long, and you can instead invest those FP's into other GB's.