I'd be very worried about brain development and health. I suspect they are making a big mistake, but its especially so for children.
https://www.tandfonline.com/doi/full/10.1080/10408398.2018.1...
> The present paper argues that the Academy of Nutrition and Dietetics ignores or gives short shrift to direct and indirect evidence that vegetarianism may be associated with serious risks for brain and body development in fetuses and children. Regular supplementation with iron, zinc, and B12 will not mitigate all of these risks. Consequently, we cannot say decisively that vegetarianism or veganism is safe for children.
I seriously recommend you read the entire review. I do not think it's something that can be trivially solved with supplementation. Eg:
> The AND says that “[v]egans must regularly consume…B-12-fortified foods or B-12-containing supplements,” and “[m]ost vegetarians should” do the same (Melina, Craig, and Levin 2016). The results of Herrmann et al. (2003) suggest that even with supplementation vegans may still tend to cluster in the deficient-to-borderline-deficient range. Vegetarians can achieve adequate B12 levels with supplementation, but some are still in the deficient and borderline-deficient range. Whether it is realistic for vegetarians/vegans to maintain adequate B12 levels throughout their entire childhood via supplementation is an open question.
> The consequences of B12 deficiency in childhood for brain and body development are extensive, severe, and can be irreversible. Potential consequences include (among many others) impaired cognitive development/school performance, depression, weakness, fatigue, nerve damage, and failure to thrive (Graham, Arvela, and Wise 1992; Rasmussen, Fernhoff, and Scanlon 2001). Breastfeeding infants whose mothers are vegetarian/vegan are also known to be at risk for B12 deficiency (Graham, Arvela, and Wise 1992; Kühne, Bubl, and Baumgartner 1991; Roschitz et al. 2005; von Schenck, Bender-Götze, and Koletzko 1997).