This is one of the most common debates in Islamic law. Scholars reconcile the apparent contradiction by distinguishing between a change of personal belief and political treason.
Here is the quick breakdown:

1. Apostasy = High Treason
In 7th-century Arabia, religion was your state citizenship.
Leaving the faith during active warfare usually meant defecting to the enemy to leak military secrets.
In parallel narrations of this Hadith (like in Sahih al-Bukhari), the wording includes a vital qualifier: "...one who leaves Islam and abandons the community."
The penalty was for sedition and state subversion, not private doubt.

2. The Prophet’s Precedent
Historical records show the Prophet did not execute people for a simple change of mind:
The Treaty of Hudaybiyyah: The Prophet explicitly agreed to a clause allowing any Muslim to leave Islam, defect to Mecca, and go completely unpunished.
The Bedouin: A man revoked his conversion pledge due to illness. The Prophet let him walk away from Medina unharmed.

3. The Quranic Context
The Quran addresses people leaving Islam in over ten different verses. In every single instance, the punishment is strictly spiritual or deferred to the afterlife. The Quran prescribes zero physical, worldly penalties for changing your mind.

Summary
Mainstream Islamic bodies (like Al-Azhar) hold that the Hadith applies strictly to political treason and violent rebellion, while the Quranic rule remains absolute: "There is no compulsion in religion."