He's not just 'someone unrelated' though, is he? He's the person who actually did the parenting, who put in the dad work. Makes him dad in my book. And it's depressing to see how many posters don't value that at all.
As most people have said, it's her choice and you have to go with it. I do wonder though how she'd feel if your dad, her stepdad, stopped behaving like a dad, didn't come to birthday gatherings, didn't plan to leave her any part of his assets, because she's 'not his daughter'. I bet she wouldn't feel happy about that.
@PullTheBricksDown
We don’t know what kind of parenting he did... All we know is that his step-daughter “got on” with him and has chosen someone else to walk her down the aisle.
Given the OP’s tone and sneeriness toward her sister’s family and choices it’s quite possible the grudge grew up as the abject outsider in that family. She has never called him Dad or referred to him as Dad - that’s very telling.
If the step-dad stopped attending his step-child’s birthday gatherings then that would say far, far more about him than her.
The OP has quite clearly downplayed her sister’s relationship with her Dad’s family given the bride is sufficiently close to have her other half-sister and cousin in the bridal party.