The most heavily debated question for fan-fictions is OOC or out of character. Its a difficult topic like order vs chaos or freedom vs discipline. Some people are purists who want zero OOC behavior. The others are fine with completely different characters with no sign of the original in them and go "Isn't it fine?". While I don't agree with the first, I can at least understand it. I don't want a full on repeat of the canon characters and situations in fan-fictions.
But the later is really stupid. Imagine if Shingeki no Kyojin (or Juijutsu Kaisen or any other story with a trio of 2 boys and 1 girl) has the main characters renamed as Harry Potter, Ronald Weasley and Hermione Granger. That's why I try to follow the motto of slight OOC with properly explained reasons.