Nevada, New York, Montana, Missouri, Maryland, Colorado, and Arizona all passed voter initiatives to protect women's access to health, including abortion. Some of those states aren't surprising, (e.g.: New York), but there's some fairly red states in there.
Nebraska's petition failed 51 to 49%; that's very close
The initiative in South Dakota' (a pretty conservative state) failed 59 to 41%. That's not as close, but it's a really red state.
Florida's initiative got 57% of the vote, but didn't pass because 66% was required to pass.
Even in red states the pro-rights groups are a very significant factor.
Dismissing pro-rights people as "only white liberal women" doesn't seem fair.