I get the feeling she doesn't die because this appears to be already fairly fictionalized if it only takes place in the summer of '69 (she was pregnant that summer, tragically so when she was murdered within weeks of her due date).
My guess it is a celebration of Sharon Tate and what she represented about the "Youth Generation" at that time. Either she survives or we simply don't talk about the murders at all (or at the least don't show them). My guess is trying to reclaim Sharon Tate for her life instead of her death is why her sister approved.
As for Manson, I am fine with him getting killed off in this film. I don't know if they'd do it, but they're obviously shooting at the farm Manson's cult lived on (you see Pitt's character riding a horse through it), so it's easy to imagine a "manslaughter" situation occurring. Yes, there would need to be a thematic logic to it, which in the case of Basterds was the power of cinema doing what we wish we could've done ourselves in '44. But Hitler orchestrated and planed the murder of millions and millions of people. If folks are okay with Tarantino changing his fate in history, I don't see why it's offensive with Manson too. Maybe Sharon killing him is too far, but I wonder if she will represent the era as so many have retroactively made her be the symbol of? If so, maybe the theme might just be let's not focus how this world ended but why it was wonderful when it was there.