I voted Marcus off the island because he ate the last hidden mango.

"Because" introduces the reason. "So" would incorrectly introduce a result, and "therefore" is a conjunctive adverb that requires different punctuation (usually a semicolon).

Since we had all agreed to share the secret food stash, his betrayal was absolutely unforgivable.

"Since" correctly introduces a dependent adverb clause at the beginning of the sentence. "Therefore" and "Consequently" cannot be used to join a dependent clause to an independent clause in this way.

I feel absolutely no guilt about my decision, as he would have done the exact same thing to me!

"As" is a subordinating conjunction introducing the reason. "Due to" is a preposition and cannot be followed by a full clause.