I understand that animal sacrifice is a religious practice that was common in antiquity, but are there any religious activities practiced today which are incompatible with veganism? And if so, are there any religious which require performance of non-vegan activities that would make the religion incompatible with veganism?
Animal sacrifice was common in antiquity, and unfortunately it is still practiced today. One reason many African folk religions, like Vodou/Vodoun, Candomble, and Santeria get such a bad rap is the continued practice of animal sacrifice; ironically, many people who don't think twice about killing animals for food loudly condemn the practice of killing animals in ritual. (While I realize that these religions are demonized for multiple reasons, animal sacrifice is not least among them.)
As for to what extent these practices are required, admittedly I've never been part of any of them but from my limited understanding, sacrifices are usually performed for magic purposes rather than a more prayer/worship context. You can check out the pagan section of Patheos for articles and information about some of these.
Many orthodox Jews celebrate their and ancient rituals. An example would be the passover ceremony which requires eating a lamb.
Not only is lamb involved but other foods such as fish and egg are involved traditionally.
There is such a thing as a Jewish vegetarianism and they have their own unique recipes for passover.