The people saying Yuffie will steal your materia and that'd be okay are totally underestimating how much that will make people HATE Yuffie.
You can't simply get over a character erasing hard progress and be expected to care about them afterwards, over half the playerbase will absolutely despise her unconditionally for the entire rest of the Remake series, even though she was only used as an excuse for a lack of carry over, because she has to take the responsibility for that in the story.
They can't afford to spend time developing an optional party member into a non-optional one and have everyone hate them. Hope had justifiable reasons why he was the way he was in FFXIII, and a ton of people couldn't get over the "Crybaby asshole," who witnessed one of the party members drop their mom to their death.
He grew, and became pretty great, but that first impression of how he was before development totally poisoned the well because most people who play games and engage in community memes never get past that first impression if it makes the character unlikeable. You even have purposely unlikeable or asshole characters who bring a game down even if their bad behaviour is played out and condemned, because even showing stuff like racism and lgbt-phobia existing is felt by a ton of people as a "commendation" of their bad actions, though that's a much worse conversation for another thread.
So, Yuffie shouldn't steal their materia and "Lose it," selling it or something, that doesn't even make sense for her character. She would steal materia, obviously, but the reason why would keep her from ever selling it. It makes little sense unless they just have her holding onto all your materia forever, and do it again for part 3 and never return them, which isn't fair and didn't happen like that in the OG.
I think, if they don't let you carry over Materia due to circumstances like Console differences and such, they will give you copies of all the missable or important materia from Part 1, and a baseline of materia already leveled a bit, while unlocking new levels for materia to be unlocked.
They may dole out most carried over (storywise if not actually carrying over) materia as the beginning portions go, which could be a way to properly reintergrate Remake's materia, and Yuffie if handled well, though it's doubtful the result would be different for anyone who wants to hate the character.
My preference would be full carry over, with the max level of 50 from the previous game accounted for to allow you to fight the Midgar Zolom as a big tough optional battle right out the gate rather then needing to come back later, but depending on how they handle these next parts it might not be possible, which is a shame.
