When secular Leftist organizations (that is, all Western governments and all major social institutions) intend to impose new rules that require Christians to do that which real Christians cannot do - or require Christians to stop doing what real Christians must do - then there is no obligation for Christians to engage in debate, discussion or explanation with those who do not share Christian premises: to do so is indeed counter-productive, since it carries the message that if the secular Leftists come up with enough strong enough arguments, then Christians will change their minds.
All that Christians need to and should do is to make a single clear and unambiguous statement on the matter: either that we will not do what we should not do; or that we will continue to do what we ought to do - to the utmost of our abilities.
What follows and how it all pans-out is, in a sense, none of our business.
We cannot, cannot be expected to, and should not even try to re-organize and reform the whole secular Leftist mainstream world: that is not our business, and it is the kind of business that prevents us doing our real business.
We must just do, or not do; and wait patiently see see what happens, and pray to bear it as best we may.
The above is not a strategy carefully crafted for success - who knows how things will unfold? It is simply a matter of taking responsibility for that for which we are responsible; and not for that for which we are not.