“I keep coming back to the hadith that whoever changes his religion should be killed. I cannot read it as anything except a threat aimed at me.”

Start with tonight. Doubting is an offence nowhere. Questioning is an offence nowhere. Reading this page is an offence nowhere. Whatever that sentence has come to mean in your mind at 2am, it does not reach a person who is unsure, and you are not what it is about.

The ruling you encountered is real and it has a context: it was formed when leaving the religion meant defecting from a political community at war, and the jurists who transmitted it attached conditions and distinctions to it across the centuries. Every pre-modern confessional state, Christian ones very much included, treated defection from the faith as treason. That does not settle the question, and it is why the question is debated among Muslim scholars today, with serious voices arguing the ruling concerns treason against a polity rather than private belief, under the Qur'anic principle that there is no compulsion in religion.

The rebuttal below takes the history properly. The fear itself is a separate matter, and it deserves its own page on this site; do not carry it alone.