The Inquisition was not after shifters (officially)
Shifters are OKed, officially, by the Church of the Silver Flame. Some tainted heritage, but generations of natural shifters have, in the Church’s official view, cleansed the race. They do not spread the curse of lycanthropy, which was the impetus for the Inquisition in the first place (afflicted lycanthropes began, for unknown reasons, to spread the curse the same as natural lycanthropes). There are even shifters who are members in good standing within the Church of the Silver Flame.
That said, many, many inquisitors were not terribly concerned about “getting it right.” Given their views on the afterlife, a faith in the Silver Flame is very compatible with a “kill ’em all and let the Flame sort it out” mentality. And since they were effectively invading the Eldeen Reaches (then a part of Aundair, but the populace, particularly shifters, did not identify much as Aundairan), plenty of non-lycanthropes responded to the Inquisition by attacking the inquisitors. Many inquisitors were not inclined to pay too much attention to the technical differences between the types of fur and fangs that attacked them.
And so the Silver Flame is very unwelcome in the Eldeen Reaches. In the deeper parts of the great forest, openly displaying the Flame is a good way to get quietly stabbed and thrown in a bog somewhere. Many, many shifters accuse the Church of attempted genocide. More than a few of the inquisitors would be guilty, too.
But not all. Many, probably most, inquisitors were honest and sincere in their beliefs and in their duty. They took the official proclamations of the Church seriously, learned the distinction between shifter and lycanthrope, and took pains to avoid attacking any but the anathema, even those who attacked them. Many of the most brutal inquisitors were actually tried and convicted for their crimes by the Church itself, though many more avoided notice.
So long as the inquisitor in the party is true to the official teachings of the Church, and acknowledged those teachings during the inquisition, he should have no animosity towards any shifter party members. There may even be remorse for those shifters who lost their lives or livelihood due to the indiscretions of overzealous inquisitors.
As a shifter, you may also be quick to label any follower of the Silver Flame – never mind an actual inquisitor! – as a genocidal racist. That depends a lot on your character, and whether or not your family and friends were ever on the wrong side of a misguided inquisitor during the Inquisition. But the Inquisition was also 166 years ago: especially for those not directly affected by the Church’s crimes, dialog and understanding may be possible.