Muslims actually believe everyone is born a Muslim,
Actually, its "sinless" not "muslim." We believe that if a newborn baby dies s/he'll go straight to heaven, as no sins will have been committed. You dont have to be a muslim to get sent to heaven
(DOnt know about mainstreamists though)
"Those who reject Islam must be killed. If they turn back, take them and kill them wherever you find them"
That was part of the law during early Islam. It was used to protect Islam, as very often, the few who had unconverted would begin spreading lies about Islam (and Im talking actual lies, not misinterpretations or whatever) for example: that muslims worship mohammad and stuff. However, people who simply unconverted and were still friendly towards Islam were treated normally. This is the punishment for Apostasy.
The Ahmadi view (taken from the book "Murder in the name of Allah" by Mirza Tahir Ahmad - despite the name, it renounces any claims that Islam supports killing and terrorism by using the Quran):
The Quran defines an apostate:
They will not stop fighting you until they turn you back from your faith, if they can. The works of those from among you who turn back from their faith and die in a state of disbelieve shall be vain in this world and the next. These are the inmates of the fire, and there shll they abide - 2:218
Anybody who unconverts has a right to do so, and no-one can declare him an apostate apart from himself. Nowhere in the Quran has this been granted to others.
What this means is, people are free to renounce their faith, but not to impose their renounciation on others.
Hence, an apostate is not someone who unconverts, but who unconverts and then forces other people to unconvert against their will.
When it comes to unconverting simply, there is no mention of any punishment for them.