This sentence talks about capability.
I can never do that.
This sentence talks about a choice. A personal preference maybe?
I will never do that.
Is this correct or can we use it interchangeably?
You shouldn't be using it interchangeably. Like you said, one is about ability while the other one is about choice. It's the same thing when you're using 'may'.
Is 'capability' the only meaning that holds. Could 'can' not hold a meaning of "it's not possible for me to do that"?
A: Are you leaving your wife?
B: I can never do that.
Of course, for some that would also entail that they don't have the capability, the strength, the personal resolve to leave the wife, but I can envision a scenario where the person is completely capable knows that it's not possible.