I had sort of mixed feelings on Teagan in Trespasser.
On the one hand, I thought his position on the Wardens was unexpectedly extreme because Alistair and the HoF ruled together at the end of DA:O (in my game at least)...it seemed a tad illogical to me, given the family relations there. However, the Wardens did turn to demons and were unwittingly part of Corypheus's plans in DA:I just two years ago. Now I ultimately gave the DA:I Wardens the chance to redeem themselves (and as Cyril pointed out, they've made up for things), so yes, they basically joined the Inquisition in DA:I when I chose to spare them.
Furthermore, these DA:I Wardens actually were Orlesian Wardens, which I suppose someone like Teagan might view as being an extension of the Orlesian Empire - and you know touchy Fereldans are about Orlais and invasion and probably any hint of political influence. At that point, I was like, well, I can kind of see how Teagan might take that poorly.
On top of that, I think he's probably extra touchy after what happened with the mages in Redcliffe. The mages were invited in to take refuge/have a semi-safe haven in (by Ali-bear, no less), but what happens? Fiona makes a honking huge error in judgment that allows Alexius to swoop in and boot Teagan out of Redcliffe. If you were deposed by an outside force that included nasty Tevinter mages, you might still be a bit touchy about potentially being usurped again in the future. Also, given that my Inquisitor is a mage, I can see it exacerbating his concerns/fears.
I was hoping he'd be more moderate and more rational, but I don't hate Teagan for freaking out. At any rate, I definitely agree about the hat probably making him grumpier than he might otherwise be, heh.