Well, if Harry has the Dark Mark in fanfiction, it would completely change his relationship with the wizarding world. He'd likely be seen as a threat and be shunned. His friends might turn against him out of fear or be forced to by the Ministry. It would also make his fight against Voldemort much more complex as he'd be associated with the Death Eaters.
One consequence could be that the Death Eaters no longer sense his connection to Voldemort. This gives Harry an advantage in his fight against them as they can't track him through the Mark.
It could change the way the wizarding world views Snape. Since the Dark Mark is a symbol of his connection to the Death Eaters, its removal might make people see him as a redeemed figure. For example, the students at Hogwarts who once feared him might start to respect him more. And the Order of the Phoenix members might trust him even more fully.
One implication could be a change in how fans perceive his character. He has always been a champion against the Dark Arts, so this would seem contradictory. It might also lead to a change in the way fanfiction writers approach writing about him, perhaps exploring more morally grey areas.
The plot would change drastically. Firstly, Harry would lose the trust of many. Dumbledore might be more suspicious of him. Secondly, the Death Eaters could have different plans for him. They might try to use him as a weapon against the Order. Thirdly, Harry would have to constantly hide the mark, adding a new layer of secrecy to the story.
In some fanfictions, Harry might use powerful ancient magic that he discovers in a hidden library or from an old wizard. This magic could be specifically designed to counter the dark magic of the Dark Mark.
Some of the die - hard Death Eaters could also be antagonists. They might not trust Harry even with the Dark Mark and try to undermine him or expose his true intentions if they suspect he's not truly on their side. Bellatrix Lestrange, for example, is so fanatical about Voldemort that she would be a likely candidate to oppose Harry even if he seems to be part of the 'dark' group.
Well, it would completely change the power dynamics in the Harry Potter universe. A Sacred Gear is a powerful object from another fictional context, and if Harry had one, he might become even more of a force to be reckoned with against Voldemort. It could also lead to new and interesting magical abilities that we haven't seen in the original series.
One idea could be that Harry gets the Dark Mark by accident and has to figure out how to hide it from his friends. Maybe he discovers that the mark has some unexpected powers that he has to learn to control.
Obviously, Voldemort would be a main antagonist. Since it's the Dark Mark of Voldemort that Harry is forced to take, Voldemort would be pulling the strings, trying to make Harry do his bidding.
It might mean a big shift in the magical world's power balance. Maybe the statue was protecting something important or symbolizing a certain authority that's now lost.