The Eyes of Tammy Faye has one redeeming aspect, and that is Jessica Chastain's performance. She gives the role everything she has, and on that strength alone, I'd recommend the film. I've long been a Jessica Chastain fan (to the point where that probably biases my recommendation), and while this isn't my favorite film of hers (not even close), it's definitely one of her best performances. The movie itself though is a bit problematic, both technically and from a subject-matter point of view.
From a technical sense, I found a lot of the editing to be clunky. Part of that, i think, is that large chunks of time were not shot/scripted, and the film glosses over things that seem like they would be important, but aren't covered at all. Two examples, in spoilers:
My other issue with the opening framing scene referenced above, is that it's not clear that it's the same event as the final scene. Which, it feels like it should be. Again, just feels like an editing issue.
In terms of performances, as I said, this is Chastain's showpiece, and she nails it. With regards to Andrew Garfield, I'm still undecided. I can't resolve in my own head whether his performance is just a caricature, or whether Jim Bakker was such a caricature himself that Garfield's performance is actually genius. But Tammy Faye was a caricature too, yet Chastain doesn't play her that way. Cherry Jones (as Tammy Faye's mother), and Vincent D'Onofrio (as Falwell) are both great, but in fairly one-note performances.
Ultimately, the movie it reminded me of most was I, Tonya. Over the last few years, there have been several biopics/bio-limited series attempting to rehabilitate maligned female cultural icons of the 80's and 90's: I, Tonya, American Crime Story season 1 and 3, and this film, for example. Some of those women (Marcia Clark and Monica Lewinsky) were treated unfairly. But just like Tonya Harding, Tammy Faye Bakker was guilty of her crimes. And this film makes it clear factually that she's guilty, but once the audience to feel emotionally that she's not. It's an off-putting dichotomy. I didn't like that aspect of I, Tonya, and I don't like it here.
Overall, if you like Jessica Chastain, see this film. If you don't, probably don't.