Kagha isn't justified in what she is doing, although she feels the opposite is true. That is kind of the entire point of her character. She is a druid, but with extremist and xenophobic leanings.
How is she not justified? You are projecting your views on her. According to her own religion she is well within her rights to do exactly what she does, and if the ritual works that pretty much means that Sylvanus approves. Again, xenophobia against extraplanar outsiders is not something I would describe as "wrong" according to the value-system of a Sylvanus-worshipping druid. Sylvanus doesn't care about your morality as long as you get the job done.
Your accusation rings false.
In fact, I do not recall ever reading material that confirms your characterization of Silvanus and his faith, nor the laws of his faith. It seems like conjecture on your part, based on your personal definition of what his alignment entails.
Nor do I think druidic attitude towards outsiders is as uniform as you describe. Let us not forget that fey (dryads among them) are outsiders as well.
Finally, I do not remember all the details of the druidic ritual, but druidic magic is not in and of itself divine in nature, and therefore not dependent on the approval of any god. Further, even for clerics, it is not common for a god to immediately thwart magic that is cast in a way that contradicts the tenets of their faith. Rather, withholding magic happens as a consequence of, often repeated, misconduct of their faithful.
Lastly, the ritual Kagha wants to perform and Silvanus's approval thereof are independent of her hostility towards the tieflings and her treatment of Arabella.
Kagha may reject common morality, reasoning based on her faith or otherwise. But that does not, in fact, absolve them of their immoral nature. After all, any evil character could use the same slippery slope if that were true.
TL;DR: Kagha a bad bitch