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How can you impose capital punishment for speaking an opinion against Islam?

You can very well, when it's about blaspheming Allah or His Holy Prophet

Where is the Shari'a basis?

I'm sure other brothers will provide these insha'Allah.

Yes, their opinions are wrong if their opinions consist of cursing Islam, but it is up to Allah to punish in this case.

Allah Himself ordered us through His Holy Prophet that certain crimes shall be punished already in this life, other than in the Hereafter.
That's why we have punishments in this life, and also the reason why criminals are arrested, instead of being said " it is up to Allah to punish you, now you may go on keeping committing your filthy crimes, my dear".

The Qur'an forbids compulsion in the religion, and this counts as compulsion. Your understanding is wrong.
That very famous (and nowadays very misinterpreted) ayah refers to accepting Islam: it can't be forced on anyone to enter in Islam, it has to be a free choice.
But then, once in Islam, there are various instances in which one may be coerced by a Qadi to do certain things.