Is it true that the Sharee'ah penalty code cannot be applied in a multi-religion country, even if Muslims rule and represent 85% of the population? Some scholars maintain this ruling.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

It is the duty of the Muslims’ ruler, whether they are the majority or minority, to apply the law of Allaah The Almighty. It is impermissible for him to not apply the Shareea'h code, even if  the Muslims are a minority, on the pretext that applying it would lead to greater corruption.  Allaah The Almighty is the One who designed these laws, and He is the One who  created mankind, so He is the One who knows what suits them best. Allaah The Almighty Says (what means):  {Does He who created not know, while He is the Subtle, the Acquainted?} [Quran 67:14]

Allaah The Almighty is Merciful and His orders never burden anyone and are never impossible to implement. Is there greater corruption than bloodshed, rape, mixing up of kinship and the ruin of the mind that is the gift of Allaah The Almighty to mankind?

 There is no doubt that failing to apply the Sharee'ah penal code increases the crime rate and that is what is happening nowadays, as the  law of Allaah The Almighty is substituted with unjust, manmade laws.

It is important to mention that applying these rules or most of them should be restricted to Muslim citizens. They are not to be applied to non-Muslims, unless they choose to go to an Islamic court. In such a case, the court may or may not judge. If it judges, it should be just. In fact, for more than thirteen centuries, non-Muslim communities had been living peacefully under the Muslim rule and their rights had been preserved and they enjoyed freedom of worship according to certain  guidelines  that cannot be comprehensively defined within this reply, but they are mentioned in detail in Fiqh (jurisprudential) references.

Allaah Knows best.