Christians have defied other governments in history by following what we believe in the face of very cruel persecution yet we not only survived but thrived. If those who remained true to the faith did not submit then what makes you think we will now.? I personally have no intention of submitting to these new made-up laws.
"Liberty" is not compelling people to act against their conscience. Your comparison of Christianity and Shari'a Law is grossly inaccurate and based on your own prejudices. Islam wants to bring the world into "submission" (which is what Islam means), financially, legally, politically and socially. This means no wine, no parties, that women must wear burkas and be subjugated to men. "They are tilth" Muhammed said, (that is, they are like tilled farm land ready for seed to be planted in) "Do with them as you will" Under Islamic rule People of the Book (Jews and Christians) will have to be subjugated and they will have to pay a special tax called the Jizla "in humility" and servility. Humiliation is the primary goal of this. Perhaps you would rather live in that culture than with oppressive Christians who just want to practice their faith by not following certain procedures. But you say Christians want the same thing as Muslims.
YOU are now on the side of the oppressors who wish to "compel" people to comply to objectionable laws under penalty of being deprived of their property and livelihood. By what moral authority do you do so - on the basis of nothing more than the fact that five out of four lawyers who happen to hold your opinion have conjured from thin air out of the constitution. In reality it is not there. It never was. However, because it is now legal it is good, right and proper and everyone had better actively "submit" Perhaps we should be forced to compensate society for our non-compliance by paying for our hate-views via a secular Jizla.