There are only about two things about the Pirates of the Caribbean film franchise that seem certain at this point. One is that there will be a future for the franchise. At least two movies are currently in some form of development. The other thing that seems certain is that Captain Jack Sparrow will not be part of that future. Every indication is that Disney has decided to take the films in a new direction and that Johnny Depp, who has made more headlines for his legal battles than his film roles in the last couple of years, is not part of that direction.
With Pirates of the Caribbean being a multi-billion dollar franchise, it has a lot of fans. And many of those fans like the movies just the way they have been, including Johnny Depp. A petition was started some time ago, when it was first reported that the Pirates movies would receive a "reboot," asking that Disney not replace Johnny Depp in the films. Last November, when Depp walked away from his role in the Fantastic Beasts movies, the petition was around 300,000 signatures, but signatures have continued to be added and now it stands at over 475,000. It seems certain now that the current goal of 500,000 will be reached.
Needless to say, that's a lot of people who care enough about Pirates of the Caribbean and Johnny Depp to sign the petition. On the one hand, it's unlikely that such a move will actually sway Disney to change its mind on this topic. At the same time, a petition of this size also will presumably not go entirely unnoticed by the House of Mouse.
The increase in signatories may have come in part due to some softening of language in the petition. Originally the text stated that those signing would not buy tickets to a future Pirates of the Caribbean movie that did not include Johnny Depp, but that wording has been removed. Now the petition is more of a statement of general support for Depp and the character of Jack Sparrow. It now says that Depp needs to be brought back to the series unless Depp himself willing walks away.
That part seems unlikely. Part of Johnny Depp's defamation lawsuit against ex-wife Amber Heard is predicated on the idea that Heard's Washington Post newspaper editorial is the specific reason Depp lost the role of Jack Sparrow. A lawsuit would seem to indicate he did not leave the role willingly and would not have done so.
It's been reported that even a simple cameo for Johnny Depp in a future Pirates of the Caribbean film has been ruled out by Disney and that seems fairly definitive. The franchise will live on, in large part thanks to the work Johnny Depp had done previously, but it seems certain it will go forward without him.