I believe what your concern is, and correct me if I am in error, how and/or what does the Catholic Church teach as regards the ever encroaching secular world and/or government(s)? Paraphrase: How are Catholics to live in increasingly secular societies where the defintion of secular is: the removal of, ignoring of, desired dissection of, limited speech to address faith and the general movement to silence faith and Catholicism from all forms of government and public life. Private only.
Well the basic position is that “if” what the “State , i.e. Secularism” is proposing is not against any teachings of the Catholic Church, then it is acceptable, we can participate. “If” however, it is against a teaching of the Catholic Church, we may not participate, i.e. abortion. And “if” such a secular program becomes mandatory, i.e. open abortions in all hospitals by all doctors without a conscsious clause, then we still cannot particpate, and at that time, all catholic doctors, nurses, administrators, secretaries etc, who would be working for such a hospital and would be in the line of work that would contribute toward abortion have the moral responsibililty to resist. To resist, does not mean armed struggle, it means not performing the work. And if this resistance caused their termination, then so be it.
I used abortion as an example, but it would apply to any such mandatory government program that was in opposition to the teaching of the church.