Sure, but there's a fundamental difference between christianity in culture and promoting female genital mutilation or denying reproductive rights.

America isn’t a “secular” nation. It’s a religiously pluralistic nation. That means that all of the various non-falsifiable moral ideologies, from Christianity to Islam to secular humanism, are on equal political footing. If more people prioritize the mother’s invisible, non-falsifiable “right to bodily autonomy” over the fetus’s invisible, non-falsifiable “right to life” then you can permit abortion. If the opposite is true, you can ban it.

> Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof …

The United States government, which is what we’re discussing is absolutely a secular body. The various religions or non-religions of the citizenry are irrelevant, constitutionally.

The first part just means that Congress cannot regulate established state churches (https://live-bri-dos.pantheonsite.io/activities/handout-c-ma...), while the second states that Congress cannot prohibit people from practicing their religion.

What the first amendment doesn’t do is exclude moral beliefs rooted in religion from being the basis of public policy. If the government can regulate conduct that kills living things, then it’s immaterial whether any particular legislation is rooted in the moral framework of Christianity or Islam or Feminism. In the American system, all moral frameworks, whether rooted in religion or not, are on equal footing. That’s distinct from secularism, as practiced by France and formerly Turkey, where religious philosophy is singled out and excluded from the public sphere.

> The first part just means that Congress cannot regulate established state churches

Err, no, that's a common misunderstanding.

The Establishment Clause of the First Amendment prohibits government from encouraging or promoting ("establishing") religion in any way.

It's there to forbid the creation of an official state religion (eg: the Church of England being created to replace the Catholic church back in the day).

See:

https://www.aclu.org/other/your-right-religious-freedom

Regardless of what the constitution says, it's a little naive to think that US law (especially state law in many jurisdictions) isn't heavily influenced by religion, mostly that of various Christian sects.