Conversely, the notion of a “right to abortion” or a “right to bodily autonomy” is for all practical purposes a religious view. It’s a belief about the nature of human society and the value of human life in its various stages.

I'm a strong proponent of the right to freedom of speech (and I'm pro-choice), but we have to be clear about the fact that these are derived from axioms, which are by definition maxims derived from subjective leaps of faith and not evidence-based objectivity.

I think that's Rayiner's point; you can't admonish people deriving philosophical views from the theistic beliefs and value systems they practice when the opposing side of those views are essentially derived from secular/atheistic beliefs and value systems. At some point in the chain of derived arguments and justifications, you arrive at an axiom whose only justification is "because I believe this should be so" or "because my in-group believes this should be so" or "because <authority figure> believes this should be so" — it's still a leap of faith.

"Humanism" is just another subjective belief system, and its adherents are no more immune to the forces of tribalism and faith-based reasoning as adherents of older belief systems.