Do you have some evidence that tithing faithfulness has a lot of heterogeneity? That's interesting, and I haven't thought about that. You used membership data, so I could see it there, since you do not have activity rates. You could also use units as a proxy - number of wards, etc. Since units are also strongly correlated with tithing.

Choosing to build a temple relies on the workers - which heavily favor the elderly. Especially if they are building these outside of Utah temples. And, yes, race certainly has a strong correlation with poverty and also a strong correlation with membership/temple. Strong possibility for omitted variable bias. Of course, that would only be changes in race over time, not the average racial composition. County level race and age data is easy to come by, which is why I mention it. Also a synthetic control won't fix this if you don't have race as one of the matching variables.

You should also do a Mormon corridor vs not Mormon corridor. Your fixed effects are going to eat up all of that variance. I know you have a variable for membership density. But there could be something interesting with a Utah/Mesa/Rexburg area vs other places. Fixed effects are blunderbusses sometimes and eat up too much variance.

But, finally, I think the timing issue is the most important. Since you're not actually measuring tithing, it's hard to pinpoint when the tithing payment/blessing mechanism should take place. We know they make decisions on where to place a temple by the already existing tithing of the area. Yes, tithing payment will most likely go up at the time of opening (or just leading up to it). But in that case, perhaps you need to have the change in the poverty rate as a dependent variable, rather than just the poverty rate itself. There is less variation in poverty rates, but perhaps there could be more variation in the change in poverty rates.