What is a good substitute that is less localized than "secular"?

I am having trouble using the term "secular" to convey a sense of bringing a religiously neutral ground to government, society, and culture. What term is better than "secular", that is less localized than the US-connotative sense, but conveys the same general meaning to multiple countries?

Secularism is often denoted the same, but from country to country it is practiced on a sliding scale in terms of how truly neutral laws are. Some of us on the Atheism.se are trying to broaden the scope of the site and are interested in methods for doing this. The usage of "secular" (that I am looking for) should convey taking secularism and using it as a tool for atheist questions to hone in on issues regarding equal rights, activism, promotion.

Secular is perfect as far as I can see. It carries no 'local' connotations. You might perhaps use 'humanist'.

If you are looking for a term to convey the opposite of superstition, the broader process of organising society according to non-superstitious principles, you might use "rationalisation" and "rational", or perhaps "evidence-based", "empiricism", and "science". But you've probably already considered those terms.