No compromise in matters of Deen:
"If you obey the majority of those on earth, they will make you lose the path of Allah. They follow nothing but whims, and they do nothing but make conjectures."
So Muslims need not worry too much about 'public opinion' as the kuffar will never like or approve of the Muslims following Shari'a.
They will continue to make demands from us to keep diluting our Deen till nothing is left of it!
"...The shaytans inspire their friends to dispute with you. If you obeyed them you would then be idolaters." 6:121
So these kuffar will keep disputing with us regarding the different aspects of Islam. And if we obey them we will loose our Emaan itself and become mushrik like them.
Allah clearly warns us the consequences of diluting our Deen to appease others:
" And never will the Jews or the Christians approve of you until you follow their religion. Say, "Indeed, the guidance of Allah is the [only] guidance." If you were to follow their desires after what has come to you of knowledge, you would have against Allah no protector or helper." 2:120.
Their religion may be Christianity or Judaism or secularism-athiesm or whatever! They will try their utmost to make us adopt it by force if necessary. The history of colonialism and the current era neo-colonial projects and the media war against Islam all testify to it.