I suspect that there may be secularists that will answer your question in a different fashion, but to me secularism is the rejection of an "other" or "alternative level of existence" to the material existence we share. Accordingly, there can be no appeal to some outside or supernatural being, power, or entity to resolve injustices or to improve human well-being. If our social and environmental problems are to be resolved, they will have to be resolved by human reason, experimentation, and cooperation.
A secularist state would, therefore, tolerate religious opinions without endorsing or encouraging them. A secularist state would be more concerned with empirical evidence and measurable outcomes. The problem, of course, is that tolerance of religious ideology cannot be extended so far as to respect the foolishness of unsupported opinions, absurd moral dictates, or religious bigotry and hate.
This, of course, is part speculation on my part. I am not aware of any nation-state that has achieved secularism as I understand it. Ruling elites find some way to imply some kind of divine endorsement - even if it is only an ideology with a ghost-in-the-machine - to support their power and privilege.
Secular states do not favour particular religions, but provide security that all religions can be followed without persecution and other disadvantges as long as religious groups are following particular rules (e.g. do not use / promote violence). Secularism to me also means that states treat all religious groups in the same way when providing resources. This way needs to be negotiated in society and can look differently in different countries, but should be rational, transparent and not following discriminatory methods. Secularlism also should try to integrate important religious groups in mainstream societies. In Fiji e.g. Christian, Hindu and Muslim holidays are public holidays and honest effort is to celebrate in the country and to let people from other religions participate.... I personally feel that this is a very important feature as it brings people from different religions together.....
There are many meanings of secularism. In democracies there are at least three major families of secularism. One which promotes neutrality toward all religions, one which demands full separation between religion and and state--which is called the Jeffersonian Wall in the US, and the French-style Laicite system. Communism was more anti-religious. Each of these forms of secularism has different assumptions and demands.
I really like the French system. It keeps the public square free from religion while allowing the peaceful coexistence of all religions. I completely agree with Peter Kindle that “tolerance of religious ideology cannot be extended so far as to respect the foolishness of unsupported opinions, absurd moral dictates, or religious bigotry and hate.” The French exemplify Peter’s point perfectly.
What the religious right calls ”persecution” is simply the just demand that they not impose their religion upon others.
“The word secularism comes from the Latin saeculum, meaning ‘a generation or this age,’ and corresponds to the Greek aeon. Its meaning extends on to connote also this ‘wordly;’ thus, its Lower Latin form saecularis means ‘worldly.’ Basically, secularism is the ideology that facilitates practice without reference to religion of any kind. When applied to politics, it is the state policy of being indifferent to political theologies, the policy of keeping politics free from religious interferences.” (The Kingdom in Secular Politics, Basileia, 2008)
1 If someone believes that secularization is an ideology, then the ideological content of those teachings that promise salvation and claim to represent the truth alone is much greater than secularism.
The term secularization has not attained worldwide significance because it proclaims a new ideology, but because the influence of the great religions has become less strong in modern times. This is not contradicted by the fact that there have been repeated attempts to stop or reverse this process - largely in vain, or, if ordered by the state, the path to religious dictatorship.
3 The path of secularization begins with the fact that in the times of religious wars, insightful philosophers, such as John Locke, recommended two important principles of peaceful coexistence:
1) Religion is free, no one must be forced into a particular religion,
2) but this freedom means that it has become a private matter
3) Tolerance towards others and other religions is a civil duty in a peaceful community
4) Religion is not weakened but strengthened by this change; it is neither forbidden nor restricted in the religious practice of groups or individuals.