The little I know:
Courts respecting such agreements is not freedom of religion, but rather courts enforcing religion. It is problematic to have the courts enforce any religious requirement. FYI, in all contracts there can be provisions that courts for various legal reasons will not enforce, why should a provision as to religious observance be special and be respected when the law does not seem to want the government to be involved in such matters. As much as this is a contract between 2 people (is this a contract or an arbitration ruling?), it is a contract as to a matter that has little to no place in a secular court.
Also it should be clarified, that usually these contracts are the result of arbitration (i.e. the Get process). As far as I am aware, arbitration awards have to follow legal principles to be upheld by a court (i.e. arbitration cannot order something that a court cannot order), so any lifestyle requirement that exceeds what a secular court would or could order should not be upheld in court.
I think that a good part of the reason in the past such requirements were upheld was under the argument that it was damaging to the children to change the lifestyle (and not that it is a violation of halacha). However, what it seems is that the court is not willing to make such a consideration a primary factor, but rather a lesser factor in considering the overall situation (e.g. maybe it is more emotionally damaging to take away the child from the mother regardless of the religious issue, so why give precedence to the religious issue? Truth is I did not read the case, so not 100% sure on all this, so a bit surmising here.