The Chantry has no anti-elven propaganda. After crushing the Dales, there were anti-Elven changes made to the Chant, but that's racism influencing the doctrine, not doctrine being racist. The elves can't rip out a country by military force and then go about being isolationist - that's just a repeat of the Dales, minus the good will that allowed them to establish the Dales in the first place in peace.
Thedas has been devastated by four blights, but only one - the first - led to any improvement in the lives of the elves. Even if the Veil tear repeats that, it will be be because the human nations as a whole are weakened, not because the Chantry ripped itself apart.
I'm willing to bet you a bigillion gold that there has never, ever, been an Elven Divine, or even a Grand Cleric. We rarely even see them as any part of the church hierarchy, instead they are often outside the hierarchy, like Leliana was. Serving the chantry but without any real authority. Ironically the place where elves can advance the furthest is in the Circles (where everyone is labelled as mage, and race becomes less important).
I'm not saying the Chant itself preaches against elves though, I'm just pointing out that the Chantry (which is distinct from the Chant itself) is racist. This is mostly because humans in general in Thedas, and especially those at the top of the food chain, tend towards racism.