If you're going to use commas for parenthetical information that can be removed, only unfortunately is unessential to the sentence.
This makes sense:
1. I'm sorry for even asking this, but it's something that has to be considered.
This does not:
2. I'm sorry for even asking this it's something that has to be considered.
In order for the second sentence to make sense without but unfortunately, you would have to add some different punctuation between this and it's in order to turn to make it understandable: a dash, a semicolon, a colon, or a period.
Depending on style, you could forego commas altogether:
I'm sorry for even asking this but unfortunately it's something that has to be considered.
However, that would be an uncommon way of presenting the sentence.
Everything being equal (assuming you interpret punctuation as part of grammar), your second sentence is actually ungrammatical—and your first sentence would be preferred by more people.
Note that even if you have a comma after but, another possible way of styling the sentence would involve no second comma but a slight rephrasing:
I'm sorry for even asking this, but it's unfortunately something that has to be considered.