My first reaction to the Chris Stewart trade was the same as many of yours: I was puzzled. But let's piece this together.
1) It's a trade for a backup catcher. The Pirates are likely replacing Tony Sanchez with Chris Stewart for part of the season, and possibly Michael McKenry with Chris Stewart for another part of the season, if Sanchez or Russell Martin gets injured. This isn't a big deal.
2) Pirates fans getting mad at a minor move because it's not a major move is among the silliest things Pirates fans do. I mean, really. We're smarter than this. It frustrates me that we haven't seen the Pirates do anything big yet this offseason, but Chris Stewart has nothing to do with that either way.
3) There's a lot about Michael McKenry's health we don't know, and at catcher, the Pirates need depth. It's got to be a little annoying for Tony Sanchez, really, that the Pirates are able to send him down because he has options, because he's an MLB-caliber catcher. But depth is important, and if you've got more of a sure thing than McKenry for your third catcher, then that's a good thing, perhaps even if you have to downgrade your backup catcher spot a bit to get it. Which I'm not even sure the Pirates are doing, because ...
4) Catcher defense still isn't widely understood. I took some flak for not acknowledging this in the bad sarcastic Yadier Molina post I wrote a few weeks ago, and those criticisms had at least some merit -- we don't really know all that well how to evaluate catcher defense, and the public attempts to quantify things like pitch-framing are still in the early stages. Teams probably have a better idea of how to do it than we do, and we know pitch-framing is an area that the Pirates have been studying at least since last offseason, because that played into the Russell Martin signing.
In other words, you can't just compare two catchers' OPS numbers to figure out who's better. Stewart has a good reputation as a pitch-framer and defender (although he struggled with wild pitches and passed balls last year). He also has a good arm. It's likely he'll frustrate Pirates fans at times with passed balls, but he should make up for that with his framing. In 2012, almost all the Yankees' catching was done by Martin and Stewart, and you can see how they did here. In 2013, Stewart ranked as the second-best pitch-framer in all of baseball, behind only Jonathan Lucroy. Martin ranked sixth. (Here's a big article that deals with Stewart's pitch-framing.)
5) The Pirates appear to know what they're doing in this area. When the Pirates signed Russell Martin last year, there was a lot of griping that sounds like a lot of the griping people are doing about Stewart today. The Pirates showed last year that they can build a good defense, and they can do it relatively cheaply. A lot of fans didn't see it coming. Even so-called "apologist" fans and commentators didn't see Martin's defense/framing in particular or the Pirates' defense in general having nearly the impact it did.
This isn't to say the Pirates should be exempt from criticism because they had one good season, obviously. But catcher defense is one area where we don't totally know what's going on, and the Pirates almost certainly know more than we do.
6) Stewart's offense is bad, and he's not that young, so he might not work out. If he doesn't, refer to point 1. In a worst-case scenario, he gets 50 or 100 bad plate appearances and the Pirates have to cut him in May or June, and then Sanchez settles in as the Pirates' backup, just as Pirates fans had hoped. It's not a big deal.