Here is a website that argues against the death penalty for blasphemy on the basis that the Quran itself does not prescribe such punishment and relies on eternal justice of Allah (hell). Another article looks at all Islamic scriptures and presents an a view point that blasphemy must be punished.
A more general view covering all nations and religions is offered on wikipedia and to my horror I have learned that some sort of penalties have only been abolished very recently in Western countries. Islamic law is treated here on wikipedia.
Attribution for graphic under CC https://en.wikipedia.org/wiki/Blasphemy
However on the core issue of Christianity and blasphemy the Quran itself passes a definite judgement that in my view is binding on devout Muslims. Hence sharing our faith and our gospel would be regarded as very offensive by many and even reading our gospels could be seen as sinful, except maybe for use in religious debate. Surah 5:17 is very clear about that.how offensive the bibles New Testament is to devout Muslims. In fairness I should mention however that different translations stronger or softer words. Only one translation uses the word blasphemy instead of disbelief or unbelief. Nevertheless Christianity is offensive to many and terror attacks are carefully targeted at Western sinfulness (as believed by devout Muslims). Read the Quranic verses here or below.
Sahih International: They have certainly disbelieved who say that Allah is Christ, the son of Mary. Say, "Then who could prevent Allah at all if He had intended to destroy Christ, the son of Mary, or his mother or everyone on the earth?" And to Allah belongs the dominion of the heavens and the earth and whatever is between them. He creates what He wills, and Allah is over all things competent.
Pickthall: They indeed have disbelieved who say: Lo! Allah is the Messiah, son of Mary. Say: Who then can do aught against Allah, if He had willed to destroy the Messiah son of Mary, and his mother and everyone on earth? Allah's is the Sovereignty of the heavens and the earth and all that is between them. He createth what He will. And Allah is Able to do all things.
Yusuf Ali: In blasphemy indeed are those that say that Allah is Christ the son of Mary. Say: "Who then hath the least power against Allah, if His will were to destroy Christ the son of Mary, his mother, and all every - one that is on the earth? For to Allah belongeth the dominion of the heavens and the earth, and all that is between. He createth what He pleaseth. For Allah hath power over all things."
Shakir: Certainly they disbelieve who say: Surely, Allah-- He is the Messiah, son of Marium. Say: Who then could control anything as against Allah when He wished to destroy the Messiah son of Marium and his mother and all those on the earth? And Allah's is the kingdom of the heavens and the earth and what is between them; He creates what He pleases; and Allah has power over all things,
Muhammad Sarwar: Those who have said that the Messiah, son of Mary, is God, have, in fact, committed themselves to disbelief. (Muhammad), ask them, "Who can prevent God from destroying the Messiah, his mother and all that is in the earth?" To God belongs all that is in the heavens, the earth, and all that is between them. God creates whatever He wants and He has power over all things.
Mohsin Khan: Surely, in disbelief are they who say that Allah is the Messiah, son of Maryam (Mary). Say (O Muhammad SAW): "Who then has the least power against Allah, if He were to destroy the Messiah, son of Maryam (Mary), his mother, and all those who are on the earth together?" And to Allah belongs the dominion of the heavens and the earth, and all that is between them. He creates what He wills. And Allah is Able to do all things.
Arberry: They are unbelievers who say, 'God is the Messiah, Mary's son.' Say: 'Who then shall overrule God in any way if He desires to destroy the Messiah, Mary's son, and his mother, and all those who are on earth?' For to God belongs the kingdom of the heavens and of the earth, and all that is between them, creating what He will. God is powerful over everything.
Quran Recitation by Saad Al-G