What English adjective means "separated from religious practices"?

The answer is "secular."

An example of the word "secular" being used in a sentence is shown below:

Public schools in the United States of America are secular.

I will share my knowledge Q&A-style so that someone in the future, using a search engine asking a similar question, might find this answer.

Could use Iconoclast.

with 's' may be sceptic. But it is more like saying Public schools in the United States of America are religious disbelievers.

I suggest two words

Secular = not having any connection with religion:

”We live in an increasingly secular society, in which religion has less and less influence on our daily lives.”

Cambridge dictionary

Temporal = relating to practical matters or physical things, rather than spiritual ones

Cambridge dictionary

Or

Temporal = Relating to worldly as opposed to spiritual affairs; secular.

‘the Church did not imitate the secular rulers who thought only of temporal gain’

Oxford lexico

In the context of your question, secular seems preferable. The schools are secular, dealing only with temporal matters.