She is a completely different character, but she also isn't?
Look, its not THAT much of a stretch; its certainly not as much of a stretch as DmC's Dante was, and that game was actually released.
That aside, its still an adventure game, you still solve puzzles, and the mechanics are only better without taking away from the old.
A XCOM first-person shooter defies everything that XCOM stood for, at least in concept. The Devil May Cry reboot was developed on opposite day which is why the new Dante is the opposite of the old Dante. You could argue that that's the same thing that happened with Lara, but I think she was just toned down instead of completely changed.
Trust me, I was the first to complain that badass Lara was gone, but it turned out... Okay. Don't get me wrong though, the Tomb Raider reboot would have been far more pleasant for me if it wasn't a Tomb Raider game at all, and just a different game called The Adventures of Sharon Pare, or something.
Also, even though many of us hate resetting our minds when playing reboots, if a game is as well-done as the new Tomb Raider, you kind of want to accept it.