I see you've glossed over my question about political influence. Does the mother, or the judge, get to dictate to the father what political rhetoric or literature is discussed in front of the child? The 1st Amendment protects both political and religious speech. If you're comfortable with the judge violating the father's 1st Amendment rights with respect to religion, you must not have any problem with limitation on the father's right to political speech as well.
A children's political affiliation is not important as a child can't vote, and exposing the child to different political views different from one parent does not cause any major problems. However, most religions are mutually exclusive.
All the judge is trying to do is to keep as much peace and normalcy in the life of the child while the issues get worked out. If it was your way, every week would be going back and forth converting to Christianity, then back to judaism, then back to Christianity, then back to Judaism, etc. That is obviously not in the child's interest. The comparable issue for politics doesn't matter as the kid can't register to vote until he is 18. Your way is pure chaos and damaging to the child.