Firstly, multiple states have been preparing for the overturning of Roe v Wade, the court case which specified the right to an abortion was privacy and therefore protected. There are multiple decades-old laws on the books that says if Roe v Wade is overturned abortion is automatically outlawed in the entire state. There's no ballot-box here.
Secondly, the Supreme Court has washed its hands of multiple institutions that would allow people to vote in politicians other than politicians already in power in their respective states. The Supreme Court has struck down or otherwise narrowed national mandates curtailing racist voting policies. The Supreme Court has outright stated they will now refuse to take up any more cases about gerrymandering, which is a process where politicians get to choose who votes for them basically. This enforces that pro-choice people will always be split up into districts where anti-abortionists are the majority.
The first point creates non-democratic law activation that bans abortion, followed by curtailing the ability for people to vote against this implementation even if they are, in aggregate, the majority of the state.
Now, it's also important to follow on the third point: the united states of america is a giant country. By land mass it is larger than the entire EU. A single state will dwarf multiple countries. This means that even though you have the right to travel to a state that allows abortion, the travel is long and expensive. They will have to fly, pay money for a hotel, and also not work for a week or more.
Overall, this means a severe curtailing of abortion access to millions of people, who are disempowered as a population to participate in democracy.