eselam ~
in the minds of many, many people, "peace" is a kin to at the very least an absence of violence, the taking of life, and bloodshed. peace for many also lends itself to notions such as "live and let live", forgiveness, and kindness to people with whom one does not agree.
so for most non-Muslims, eselam, the concept of taking someone's life if they chose to leave Islam does not come across as very peaceful, gracious, forgiving, or lenient. once a life is taken, it can't come back. at least, not under normal circumstances. were you or i to be killed right now, we'd have no chance to come back, hug our loved ones, enjoy the sunshine, or live out the rest of our natural life. death in that sense is final for us humans. to take a person's life away from them for a reason such as renouncng a faith is regarded by most to be extreme, unkind, lacking in compassion, and certainly far from a peaceful measure.
but it is not like that. non muslims do not ask muslims about islam, but they ask one another. so how can that be allowed, and not only that but then us muslims are accused for their way of thinking and missinterpretations about islam, why should we be responsible for their wrong doing?
here is a good explanation from brother Fatihah for appostates in islam:
Apostacy is mentioned in several places of the qur'an (2:217, 3:86-90, 4:137, 9:66, 9:74, 16:106-109, 4:88-91 and 47:24-27) but in all of those places, the death penalty is not the prescribed punishment. In fact, the death penalty is not prescribed as a punishment for any crime except in ch.5:33 and 45 in which the reason is due to killing someone else or in self defense or causing mischief and disorder in the land or waging war against islam.
But here is the important part. In verse 34 of the same chapter we read "Except those who repent before you have them in your power. So know that Allah is Most Forgiving, Merciful".
Also in ch.2:178 the death penalty is also mentioned but is followed by the option of providing blood-money as a punishment for the victims family if they choose so instead of death.
In summary, where ever the death sentence is mentioned in the qur'an, it is an option to certain crimes, not mandatory. And if the victim repents and wants peace, we as muslims must grant it to them.
Now the issue of apostacy. In ch. 4:88-91, we are told that the muslims were in a disagreement as to how to deal with the hypocrites. You see, there is a difference between a hypocrite and an apostate. A hypocrite is one who declares themself as a muslim and/or goes about preaching to others to follow the religion of islam but all the while they them self do not practice what they preach . An apostate on the other hand is one who openly declares themself as a muslim or take the shahada but later they openly reject the religion. The solution was for the hypocrites to migrate with Muhammad as a test to their faith;(verse 89) for if they are truly muslims they should willingly accept. If they turn away, then seize them and kill them because their turning away would confirm their apostacy.
But now let's read the following verse. (Verse 90)
"Except those who are connected with a people between whom and you there is a pact, or those who come to you, while their hearts shrink from fighting you or fighting their own people. And if Allah had pleased, He could have given them power against you, then they would have surely fought you. So, if they keep aloof from you and fight you not, and make you an offer of peace, then Allah has allowed you no way against them".
This verse confirms that death is not a mandatory punishment for apostacy for if it was then Allah would not say to grant them peace if they wished to do so.
So in conclusion, the death sentence is the punishment for apostacy but we must keep in mind that if the apostates ask for peace and does not cause any war, we as muslims must grant it. Hope this helps.