By releasing a library with version 0.x, I communicate: "I consider this project to be under initial development and would advice people not to depend on in unless you want to participate in its initial development".
I don't understand why people find this difficult or controversial.
For example, sometimes projects that have a 0.y version get depended on a lot, and so moving to 1.0.0 can be super painful. This is the case with the libc crate in Rust, which the 0.1.0 -> 0.2.0 transition was super painful for the ecosystem. Even though it should be a 1.0.0 crate, it is not, because the pain of causing an ecosystem split isn't considered to be worth the version number change.
The only time you run into a problem is if you try and use values with a type from 0.1 with a function that takes a 0.2 as an argument, or whatever. Then you get a type error.