Can the future not be changed in That's So Raven/Raven's Home?

I don't remember all the episodes, but Raven and Booker often misinterpret the meaning of their visions, so that the actual events which eventually happen are different from what they expected and either hoped for or dreaded.

I don't think that I remember any episodes where they prevented their visions from happening, and I think that they often cause their visions to happen by trying to prevent them. So it seems to me that their visions are predestined and inescapable in most or all of the episodes I have seen, though someone more expert than I am might have more to say on the subject.

I also add that That's So Raven and Raven's Home are not in a "Ravenverse" of their own, but are generally considered to be part of the DCLAU, or Disney Channel Live Action Universe. That includes a number of other shows with science fiction and fantasy elements. So there should be other DCLAU shows with precognition and time travel.

I believe the Wizards in Wizards of Waverly Place, for example, have some sort of time travel and time rewind spells.

I think the time travelling girls in Best Friends Whenever have sometimes changed history and thus the present, meaning that the future is not immutable and predestined for them, even if it seems to be for Raven & Booker's visions.

Of course, the DCLAU series Girl Meets World was a sequel to Boy Meets World, which was in a universe with other TGIF shows, including Family Matters where Steve Urkel invented a time machine and where the laws of time might be different from those in Raven.

And supporters of the Tommy Westphall Universe theory include the TGIF shows in the Tommy Westphall Universe that contains possibly hundreds of TV series, including some with time travel like, allegedly, Star Trek. And in Star Trek the laws of time travel, including whether the future is predestined or can be changed, seem to be different in every single time travel episode.

Here is a link to a site with a master list of all the series they consider to be part of the Tommy Westphall Universe, which included 441 television series as of the latest update in August 2016.

According to those sites, Raven's Home is a sequel to That's So Raven, which is linked to the Suite Life of Zack and Cody, which is linked to to the Suite Life on Deck, which is linked to Jessie, which is linked to Live & Maddie, which is linked to Best Friends Whenever, which is linked to Girl Meets World, which is a sequel to Boy Meets World.

Or That's so Raven is linked to The Suite Life of Zack and Cody, which is linked to Jessie, linked to K.C. Undercover and I Didn't Do It, both linked to Austin & Ally, linked to Girl meets World, linked to Boy Meets World, linked to Sabrina the Teenage Witch, linked to Clueless, linked to Moesha, linked to The Parkers, linked to The Hughleys, linked to The Drew Carey Show, linked to Coach, linked to Newhart, linked to The Bob Newhart Show, linked to St. Elsewhere, linked to Cheers, linked to the John Larroquette Show, linked to Star Trek: The Next Generation, which is linked to all the other Star Trek shows with all their time travel stories. Star Trek is also supposed to be linked to Red Dwarf, which is supposed to be linked to Dr. Who with hundreds of time travel episodes.

Of course opinions vary on how strong a connection two different shows have to have to be considered part of the same fictional universe, so there can be different views on how many shows are int the same fictional universe as Raven and Raven's Home.

I have seen a site that claims that Star Trek is in a fictional universe with only about a dozen other shows, called Group 10, and that St. Elsewhere shares its fictional universe, called Group 2, with "only" about 94 shows instead of over 400 shows. It puts Dr. Who with all it's time travel stories in a Group 27. It has a Group 30 that includes Girl Meets World and a bunch of TGIF related shows but doesn't include the DCLAU shows.

That would tend to reduce the other time travel shows to consider when deciding if the future is immutable and preordained in That's So Raven and Raven's Home.

So the question of whether the future is predetermined and unavoidable in That's so Raven and Raven's home can get very complicated if other shows that might be counted by some persons as part of their fictional universe are also considered.

I know this answer is a little late, but I'm on a binge of random episodes of the original series and in the episode Hook Up My Space (Season 4 Episode 6), Raven has a vision near the start of the episode of Cory making a presentation to their father, and she rushes to intercept him in time to prevent it from happening. She succeeds. I think that's one of the few instances where her vision doesn't actually happen, due to her intervention.

In That's So Raven, there have been visions that have changed.

I think the point/theme of the visions in Raven's Home is more of being open to alternative interpretations of the visions or wisdom in knowing that there may be more to the story (presented in any particular vision), rather than fate/determinism vs free will. From what I recall in That's So Raven (and one episode of Cory in the House), this is also the case, but I think That's So Raven had more, but only a little more, fate/determinism vs free will themed episodes than Raven's Home did.

Here's an example where a vision has changed:

For example S02E13 Radio Heads, Raven says at the end:

Guys, just checked out the future. We're going to be friends forever.

This was based on a vision she just had, but earlier the episode, it was shown that Raven had a vision that went like:

In Season 1 Episode 2, Raven has a vision that Eddie fails a test but it doesn't come true after the teacher changes all the questions at the last minute.