There was no political blowback because the whole trial was nothing but a conspiracy to begin with.
It was foreshadowing for later revelations in the story. Thordan was setting up his big "turn into a god-king" Primal plan and the last thing he needed was Eorzea's Eikon Slayer and their meddling Scooby Gang Scion friends snooping around potentially spoiling the whole thing (especially with Lahabrea and Igeyorhm in his ear pulling his strings as well).
But he knew he couldn't just accuse the WoL of heresy as they had barely spent any time in the city (and lets face it, so soon after the Ul'dah debacle, they're not about to go quietly if a bunch of knights tried to arrest them on trumped-up charges.), so no one in the city was going to be that gullible enough to believe such a lie. So he went after the next best thing as he needed it to be credible - Alphinaud and Tataru.
Of course, that then blew up in his face when we thrashed the Heaven's Ward and humilated them in that trial by combat. As far as the court was concerned, it really was divine intervention that we prevailed, but the lack of retaliation from the Heaven's Ward was purely pragmatic. They couldn't retaliate because it would risk exposing the conspiracy, so the Heaven's Ward had to basically sit and stew and lick their wounds for a while as the Archbishop paid lip service to us while
scheming behind the scenes with his erstwhile Ascian flunkies to make his Knights of the Round summoning plan a reality.