Sorry, but I find your explanation for how this decision isn't "political" extremely lacking. To me it is based on a very narrow understanding of what politics are about.
Decisions based on religious beliefs are STILL political. Indeed, every SCOTUS decision is a political one.
Politics is about POWER. Who has it. Who doesn't. Who gets to tell others what they can and cannot do. Who has to conform to those orders.
Doesn't matter if the arrangement of power has a religious excuse behind it.
In fact, when I saw your headline (and not recalling anything about your politics), I thought, "oh no, another religious zealot."
Religious institutions are political, because they are about the arrangements of relationships of power. That, above all, is why churches should be taxed...up the wazoo, I would hope.
There is no better example of the conjunction of religion and political power than those nation states grounded on religious beliefs.
So while I suspect our politics are very similar, it seems our understanding of what counts as "political" is widely divergent.