Frankly, I think the argument to support Kennedy was pretty compelling. The first amendment allows for the free practice of any religion by the people. It makes no commentary on the government specifically censoring any religion. In fact it appears to be just the opposite. The text reads that the government has a duty to not act at all when religious expression is made by the people.
And that's all in public schools!
From Sotomayor's dissent, page 18: https://www.supremecourt.gov/opinions/21pdf/21-418_i425.pdf
It's important to note that coercion doesn't have to be explicit with observed punishments and rewards, and Sotomayor explains this quite clearly (including how courts have previously held this to be true for many years).
Like most SCOTUS opinions and dissents, these are technically well-written, accessible, and easy to read - I would encourage you to do so. They sometimes even border on enjoyable to read (although maybe I'm just weird). The case as laid out in the dissent is rather egregious, and it's shocking that the SCOTUS upheld such a clear violation of the establishment clause. It's shocking that they even heard the case to begin with.